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The Journal ,of Gear Manufoctur; ng

CONT.ENTS PA.GENO ..

!IPEATURES

COMPUTER.·AIDED SPUR 'GEAR.1I00TH DESIGN:AN AP.PLlCATION D.RIVEN APPRo.ACH m

Dr. Hormoz Zarefar, Portland State Universizy, Portland, ORDr. T. J. Lawley. University of Texas at Arlington, Ar1ington, T1.

SYSTEMATIC APPROACH TO DESIGNING PLASTIC SPUR ANDHElICAL GEARS 12

Raymond M. Paquet, Plastics Gearing Technology, lnc., Manchester, CT

HARD FINISHING ANDF.INE FINISHING - PART D 30Dr. ·)ng H.. Schriefer, Carl Hurth GmbH & Co., Munich,. West Gennany

IDE.PARTMENTS

EDITORIAL 5

GUEST EDITORIALJames R Partridge, President, AGMA

9

TECHNI.CALCALENDAR

CLASSIFIEDS

ADVERTISERS' INDEX

November/December,. 1989 Vol. 6, No.6'GEA_RTECHNOLOG .... Tbe JoumaloJ Gear .1I'I:anu(aclu.1nl (lSSN 0743-6858f i. published bimonthl.y b~ Randall Publ~htn~

Co .. Inc .. 14.25 Lu-nl. A""n"o. P. O. eo. 1426·. Elk Grove ViU~.IL. 00007. GEAR 'l'EClINOI.OCY. The Joumal ofCcar·M nufae·turin!!. Subscriphon rates are; 540.00 In the \Jnlted States, $50.00 In Canada. $55.00 In all oU! r foreign coo.nlrn:.. Second-Classpo~t;,ge pIDd at Arlington !He,!II1ts.II. and at additional "",mill!, office.

Postmaster: Send add. ress <halll!"" to..GEAR TEcCH OLOGY. The Journal of G"". Manur,aclurinQ, 1425 !..un! """nUl!. P. 0,Box 1426. Elk Gro.e Village. Ill. '60007.

rrtents <OPllTlghted by RANDALL. PBLISHING CO.. IN . 1989'. Artkl.,. appearinll In GEA~ TECHN ~OCy ''''"Y not berepnxiuc·e.d 11:1whole or in part Without 'the express permission of the 'r,ubli.she_'I'Or the author.

MANUSCRIPTS, We are- "'Qu""tmlll,,~hmc,ai 1'0,1>"''' wid1 an ed,,;;ation~1 emphasi\ for an)'One haw"!! "")/thi,,!! '10 do .....h Ih~design. manufacture. 1J5ti"!l or prooessing ,,(gears. SL.ib.MrlS",ught an solunons to specific protliCl!I5. Hl)Ianatioru 0( .........: te;;hnciingy.technlque s, de.,gns. processes, and alternative manufoc.turLnll methods. These can r'l!1lie from the "\low 10 .•. " of lie'" cutt"'l1(BACK '1'0 BASICS) to the most advanced tecnn<illlill'. Allmanuscripl!! submltted "'ill be carefully <onsid red. I-I","""""r, th PubiL.h·rassumes 00 responsibility forth. oatety or return of manuscripts, Manuscripts m.... be .accornpanled by a :!df,OIddreAed. ,,,If·sUmped.n""lop" •. and be sent to GEAR 'l'ECHNOLOCY. Tbe Journal of CeW' M.nufacturi"lt 1',0. Box 142·6. Elk ·Cro'e. IL 60009.(108) 4·31-6604.

November/Decemberl'989 3:

withlorona-

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and advancedl ONe control technology.• Computer hardware andappllcaticns software are modular to al!low the user to buy

only the required capabiUty.Tlhis makes the 3000 CC adaptable to laboratory testingor preduetien-llns inspection. -

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CIRCLE A~ ON READER REPLVCAiRO

S!KllUD TRAD;ES AIRENOT"SIECON[).IRATIE" JOBS

The society which scorns excellencein plumbing because plumbing is ahumble activity and tolerates shod-,dine . in philosophy because it is anexalted activity will have neither goodplumbing nor good philosophy.Neither its pipes nor its theories wiflhold wilter.

John W ..Gardner

The press Ir~1 ase on my desk thismorning aid, "The (precision metalwor'king) industry cannot attractenough quahfied applicants. As manyasl ,500 jobs a yea.r (in the Chicagoarea. alone) are going unfilled." So whatelse is new? That's just hard proof con-firming the suspicion many of us havehad for some time. Some of the best,most qualified and experienced peoplein our shops are reaching retirementage, and there's no one around to filiitheir spots. And, if the situation is badin the metal working trades in general.it's even more critical in the gearing in-dustry. Bing small and highly special-ized, gear m_ nufacturing attracts evenless attention and finds recruitmenthard r than the other precision metaltrades.

Why is this? Irs easy to point fingersand beat up on the education system.You know the litany by heart. "We don'tdo as well as the japanese," "Our kidslack discipline and respect. for hardwork." "Nobody knows how to teachmath and science anymore." "Thegov rnm nt isn't spending enoughmoney ani education." But surely theseare half-truths at best.

This same news release hit onsom thing that may be closer to themark. "Exp rts believe society haspush d the idea that to succeed,everyon must have a college educa-tion and has the notion the manufactur-ing jobs are second-class careers." This

time, at least, the experts are on tosomething.

If, as I do, you have late high choolor college age people in your life, andyou listen to them and their friends asthey discuss the serious business ofplanning their careers, you will eom di turbing pictures emerge. F w,

if any ofthem, even consider not goingto college. This does not necessarilyhave anything to do with a burningd sire for higher education ontheirpart.

Th y go because, "All my friends argoing," or "My parents will 'kill me if Idon't," or "You can't earn any money ifyou don't go to college." They ask,'What would I do if II didn't go to col-lege? flip hamburgers?"

And what willi they be studying at col-lege? "II dunno. Ma.rketing, I, guess.""Business." "Pre-law, maybe."

'Now, there's nothing wrong withlearning marketing, business, or prepar-ing for law school. But the fact is, thenation can use only so many marketingmanagers and business school grads,and it already has too many lawyers.(What are all these people going tomarket if there's no one around 10manufacture anything?)

What is sad and disturbing aboutthese young people is that many ofthem will go on to college, prepare for

care rs in which 'they ar only moder-ately interested, perform indifferently,and graduate fr.ankly iU-prepared to domuch of anything useful. They and/ortheir parents will be saddled with thou-sand of dollars worth of debt, and theonlly jobs they'll qualify for ar, entrylevel office positions paying less than$20,000 per year.

These young p ople are not stupid orill-disciplined, nor are thy, to us thecurrent teen-agd term, "burn-outs,"dabbling in drugs or lin troubl with thelaw, and with no IU e for or intere tinhonest work. They'r bright, eager,hard-working young rns nand womenwho are being pr ssur d by their peers,their parent, and their school guidanccounselors to think tharaspinng toanything less than a cell ge educationis to be a "fai lure," and that any job thatdoesn't require a college diploma is"second-rate" .

This is a dangrou set of mi perc p-tions, l't undervalu s many impo.rtantjobs lin our society and overvalueothers and, in th proc 55, 'kew in anegative way the number of peopleavailable to do. the jobs society needsdone ..

Don't misunde rstandl me. I believe inhigher education. Its value has b enthe subject of many of my editorialsover the last six years. Acollege duca-lion provides opportunitie that shouldbe available to very n .who. wants totake advantage of them. But it' .not thonly game in town. Contrary to whatwe, with the best of intentions, mol..,.have taught our children, not everyonehas to go to colleg to have elther a de-cent sense of self-worth or a decent jobwith a good salary and a chance foradvancement,

College is a particular kind of high reducation thai has its uses, but it can'tteach everyone everything. Not every

Icon[lnued on page 20J

INovember/Dec;smber 1989 5

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shops. CIMA Kanzaki blends heavy-dutyconstruction, a state-of-the-art control packageand premium gear shaving features into acompact package .... for a not-so-premium price.We invite your comparison ... feature-for-feature, with any heavy-duty, gear shavercapable of quality levels of ± .00004" on work-pieces to 18"0.D. In addition to exceptionalquality, quick set-ups and fast running speeds,CIMA Kanzaki will give you something else ....extra dollars in your pocket

elM, A,' Kan~ak,i will continue t,o saveyou money. When you order a

. CIMA Kanzaki 6-axis gear shaver" youget to make choices (if you want to). Choosingfamiliar controls, electrical components. hydrau-lics and other systems can make set-up, routinemaintenance or machine adjustments easy andquick with your own staff. That's right. ..most maintenance can be performed withoutexpensive contractors or factory personnel.

Great American geannakers deserveWorld Class Finishing equipmentthat REDUCES CYCLE TIMES ..

IMPROVES QUALITY and INCREASESSHOP PROFITABILITY.Ask our sales representatives for further detailsorcontact: C[MA USA, Division of GDPM, Inc.501 Southlake Blvd.Richmond VA 23236Phone (804) 794·9764FAX (804) 794-6187TELEX 6844252

TECHNICAL CALENDAR

NOVEl'VtBER 6-8, 1989'. AGMA Gear Ex-po '89, David lawrence ConventionCenter, Pittsburgh, PA. EXhibition of gearmachine tools, supplies, accessories andgear products ..For more information, eon-tact: Wendy Peidl, AGNtA, 1500 KingStreet, Suite 201, Alexandria, VA 22314 ..(703) 684-0211.

NOVE'vlBER 7~~ 1989, AGMA FaDTech-nical Meeting,. Pittsburgh,PA. Seminars ona variety of gearing subjects held in con-junction with Gear Expo '89.

NOVEMBER 29 - DECflvIBm 1.. fun-damentals of Gear Design, Seminar,University ofWIlSco.~Milwaukee.Thiscourse will cover basic design considera-tions in the development of at properlyfunctioning gear system, It is planned with'th· d '. .nd ~n .. ; .....e _esIgner, user, ano ~"IJL1'6 geartechnologist in mind. For more informa-tion,contact: Richard G. Albers, Center forContinuing Engineering EdUcation, Univer-sity of Wisconsin-Milwaukee, 929 North6th Street,. Milwaukee, WI, 53203. Ph:(414) 227-312.5.

The International T lade Commission isholding public hearings for the purpose ofassessing the competitive position of 'theU.S. gear industry in U.S. and globalmarkets. These hearings will be held onNovember 1, 1989,at 9:30 a.m, If youwish to be heard or submit a written state-ment, 1Nriteto the Secretary U.S. Interna-tional. Trade Commission, 500 E. Street,S.W., Washington, D.C., 10436.

AGMA J:eclmica1 Education Seminars,Series U. These one- or two-day seminarspresent the latest t,echniquesand informa-tion on specific topics in at small group con-text. For more Wonnationrega:rding fees.and registration contact AGMA., l5((l KingSt., Suite 201, Alexandria, VA 22314, (700)684-0211.

December $-6, 1989., Los Angeles, CALoose Gear Inspection from the Customer'sStandpoint.January 23, 1990, Cincinnati, OHGear Failure AnalysisMailch 6, 1990, Cincinnati, OHRational Gear Design and Lubricationrviay8, 1990, Los Angeles, CAControlling the Carburizing ProcessJune ~, i990, Alexandria, VAGear System Design for Noise Control

Only Albar Ipsen offers you thewidest range of heat treatingand surlace treatmentequipment for gear and geartool manufacturing.Rugged, F,lex;ibl:eAtmosphere Carburlzlng ...The LfO line is automated forJIT manufacturing and isreadily adaptable to nitemperand other carbuli2ingandnitridlng processes,Enhancedl Wear & FatigueReslstalilcefor PrecisionAerospace Gearing •..Plasma carburizing andnitriding systems provideuniform case depths forprecision surface hardening.

Maximum Tool SteelHardening ••• You can selectfrom any of three "II-lighPressure auenc'hty" vacuumfurnaces for hig·h hardness.distortion control, and crualityprocessing of even the most·geometricaUy complexgeaI,c:utt'ingtools.Increased CuttlngT,oolLite, .,. TiN Sputter IonPlating System gives yousuperior hardness, increasedlubricity and! the ability to 'cutharder materials .Call us today and tell us aboutyour application requirements.Chances are we've got thethel1Tlai processIng systemthat's nght for you ..

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CIRCLE A-S ON READER REPLY CAiRONovember/December 1989 7

CuMISSION: COMPElliNG TO W,IN

Like a lot or people, I grew up seeing the world as fairlyflat and believing that everything of importance happenedin Texas. As Igrew older, my outlook grew to include theUnited States,Canada, and Mexico. The rest of the worlddid not seem very important, if it existed at all. Unfortu-nately, IIwas not alone in this very narrow view. Manyothers in the gear business shared this perception,

Today the world is a bigger and meaner place than it ap-peared when I was growing up. In traveling to other coun-tries for my company and AGMA, I've seen our foreigncornpet.tion in both the marketplace and their factories.Our European and Asian competitors are tough. They'vedone their homework, most of it in our own back yard.

These foreign companies have grown to be true com-petltors i,nevery market. We see their footprints every-where, as foreign shipments into the u.s. and Canada con-tinue to rise. linsome cases, these companies have decidedto build, buy, or expand plants in our country. We nowhave to compete with them toe-to-toe or we stand a goodchance of "losing the farm."

AGMA's mission is to assist its members to compete moreeffectively intodays global market. The Association is do-ing this in several ways. ACMA's reports keep us better in-formed about. international economics and market trendsthat have a major impact on our members. Throughstandards-writing activities, we bring the best technicalknow-how to both national and international standards.The fall Technical Meeting, the Gear Manufacturing Sym-posiurn, and the Technical Education Seminars help passal'ong this manufacturing expertise to the gear producers.The AGMA Manufacturer's Self-Certification Programenables us to upgrade ou r skills and helps assure customersthat the best gear expertise in the world is put to work ontheir projects.

The week of meetings this year is Plittsburgh is where a lotof those efforts come together. The Fall Technical Meetinghas grown to a session that truly has an international repu-tation for excellence. At this meeting, the best design andproduction gear engineers from around the world sharetheir expertise,

JAMES R. PARlIRJUGE, current AGMA president, is VicePresident of Lufkin Industries. He is a registered professionalengineer and a member of the Texas Society of ProfessionalEngineers. He is currently a Director of AGMA and has servedas Treasurer and Senior Vice President of the association.Mr. Partridge is also an active member of the AmericanPetroleum Institute and the Society of Petroleum Engineers. Heis a graduiJte of TexasA&M' University.

ial

Just as important is what we can learn on the floor of theGear Expo in November. This event is not only the largestshow dedicated to just the gear industry - it is also thebest! There is more of the latest gear machinery and manu-facturing knowledge per square fool at the exposition thananywhere else in the world.

Together these two important events in Pittsburgh offer LIS

the chance to see"The Cutting Edge"of our technology -in design, application, and manufacturing. If you are readyto work in the competitive world of today, Gear Expo '89 isthe place to obtain the necessary tools,

We can't expect someone else to shield our hides fromthe competition we face in the market. To furnish the bestproduct and services at a competitive price, we must havethe tools to compete, help set the rules of the game, play atour best, and keep track of the score. In Pittsburgh, wehave the chance to "get down to it" and individually learnthe best way to play to win.

The alternative is not acceptable!

James R. Partidge,President, AGMA

November/DecemDel'1989 '9

Computer-Aided Spur Cear Tooth Design:An Application-Dri~en Approach

H. ZarefarPortland State University, Portland, OR

T.J. LawleyUniversity of Texas at Arlington, Arlington, TX

Abstract:Thisarticle discusses an appl.ication-

driven approach to the computer-aidedsizing o,f spur gear teeth. Themethodology is based on the index oftooth loading and the environment of ap-

AUTHORS:

DR, HORMOZ ZAREfAR is Assistant Pro-fessor of Mech'IP1ical Engineering at Port/andStat;e University, where he teaches mechanicaldesign cmd does research in the area of automa-tion-of the design of mechanical components.He received his Ph.D. in mechanical engineer"ingfrom the University of Texas at Ar.lington.where he received .the Carl W. Files Outstand-tngTeachjngA~sociateAward. Dr. Zarefarisa member of ASME, ASEE. Sigma Xi (Scienti-fic Resear;ch Society) and Pi Tau Sigma(Mechem!cal Engineering Scholastic HonorSociety).

DR. T.~. LAWLEYhas been a professor ofmechanical engineering design since 1971.Before that he was employed as a mechanicalengineering design engineer in industry for nineyears. He received his B.A. ,and B.S.M.E.degrees from Rice University and his M.S.M. E.and Ph.D. degrees from Southern MethodistUniversity. He isa member of ASME and a.registered pmfessionalengineer.

plication ofthe gear. It employs hand-book knowledge and empirical informa-tion to facilitate the design process for anovice. Resuhs show that the approach isin. agreement with the textbook data.However, this technique requires less ex-pert knowledge to arrive at the conclu-sian. The methodology has been sue-oessfully implemented as a gear toothsizing module of a parallel axis gear driveexpert system.

IntroductionThe science of gear design is one that has

been thoroughly investigated and muc-hwrittcen about, (1,2) In transmission of mo-tion via.gears, two or more axes can be ar-ranged in just about any orientation . Oneof the most common arrangements of in-put / output transmissions is the parallelaxis type, in. which the motion is transmit-ted from an input axis to a parallel outputshaft. There are two Widely used gear toothconfigur:ationJO.to achieve the parallel axisarrangement; namely, spur and helicalgear tooth designations. SpU1' gear drivesare the most 'economical way of transmis-

sion of motion between parallel axes.Recently, with extensive utilization of

digitaIcomputers in. engjneering design andanalysis. interest has been shifted towardautomation of gear design. Several at-tempts have been made in which varioustechniques for routine gear tooth designhave been ,e,omputerized.(1.4) However.these attempts have all been initiated by ex-pert gear designers and have been based. onthe individual's own methodology forthegear tooth design process.

In this article a new technique forcomputer-aided sizing of the spur geartooth is discussed ..The .approach is basedon the requirements. of the application en-vironment of the gear, while the typicaltextbook approach (3) requires that theuser be proficient in.making .key assump-tions in the design. process. Althoughlimited to spur gears, a similar approachcan be employed for the design of helicaland other types of gear teeth as well.

The ApproachIn general. design of a typical gearbox is

influenoed by the following factors:

Table 1

Minimum ib.arn'ncuof 11«1 gun,

Pinion Gear

225 Hl!: 21DM8335 HB 3OO'H~

59'HRC saHRC22~ HD 2:IDHB

I!335 HB 300HB38 HR.C 51 HIlC

225, HS 2il0 HI

II335, HD 300HB

58: HRC 58 HR.C

22S HD 2101 HI

I:335 HB 300HB

58: HRC 58HRC

60HRC 60HRC I60HRC 60HRC I

59HRC 59HRC I

591 HRC 59HRC I

3201HB PhrnnliIIlaminair

320' HB I Ny:I.on200 H.B

,Zim'I

I alloy:roo HB I Br4u"S tlf

'I aluminum

No.pinion,cycles

Uait load

N/mmlJ ."" N/lllmi Ip!I!i,

101.69 100 45 UOD1,04 150 .59 1I.i(l)2.76 400 81 l20000.48, 10 31 4,500'0.76, ue 51 5,5(1)12'.1017 !OO, ~ ,1.Il0011.58: 201), 51 5,:x1012.07 'MOl 48 ",,0001~.52 8001 69 :10,Il0010.83 r20l 24 3,M/O1.2+ ,lBO'

I31, 1,,5(1(1'

3.45 50(1,I 41 6,0001

,~U6 850 117 17,,0001•. 14 600 '6 11,0006.20 9001 124 18,0008.96 I~I 124 1&0000.3. 5(11

0.24 3S0.10 I~,

'0.110 15

Applit'ation

Turbim" driving a generator High pR'CiIion,High pl'CdlioDHi,;h ~ilion

101"10'101'

HJ b pm;iM1IHir" PfmaonHiib i-::Dion

Intc:1'IlIl comb~lion, ,rn,ginc driving!!comp~

10·lot10'

Grnua.l~.pu rpo!'t induslrial drive!.h~l i1'1l1 r rt'1:lli~'d:y 1m1(onJI IlmItH:for hOib dri,vinl!: and driven units)

Mediuml hllh pm.ionMediuMI high ~ODMedium hi!'h mcdlion

10·lot10'

Medium pm:ilionMcdillm prt'cilionMedium precision

yrg~indlUlr:ial drives, spur -hoists, kilns, mills(modcnne shock lin cI'riven units,!

.'CnMPacc, ,helical (single ~ir) II:

10"

Medium hillh IDftcisifJn\:rhu:le Ir.l.lISmIiSiun" helicalMedium bigh :PJltciJ.ioo\'"hu.le fin.! drh-e. spur

SmMl ('..m~r('ialpi!i·h·lillll' ' ipn-cl

1M.'!Ih"n S m/s' 10'I Medium :p",cisionSmall~.\d~rl

(pil' h-li'ne speedI~",Ih:lfl 2.'5, mI., Medium precision

• Spatial. arrangement of the input/out-put shafts.,

'. Input! output speed ratio.• Power transmitted (torque or horse-power / speed combination).

Table .2

Long-life,I

Vehicle gcan,high-speed gears short life a.1 maximum lorque

RalioII .Brin.ell: hardness Brine II hardness,

{mal 100 300 400 600 200 300 400 '600

I 80 50 39 35 SO 37 29 261.5 ,67 45 3,2 30 45 30 24 22'1 ,GO' 42 28 27 42 27 21 203 53 37 25 25 37 24 18, 184 49 34 24 24- 34 n 17 175 47 32 23 23 32 22 17 177 45 31 22 22 31 21 16, 16

10 43 30 21 21 30' 20 16 16

The proposed spur gear tooth designeris an application~rvencomputer programin which Ithe user identifies the nature ofcomponents, machines, or assemblieswhere the gear is to be used. It is essential-ly based on the index of tooth loading or K-factor yJ This index is a basis for initialgear tooth design; hence, the preliminarystage of the design starts with selecting aninitial K-factor from the user-definedap-plicafion environment. Based upon thespecified value of K-factor. a Bnnell hard-ness number can be 'established (Table 1).From a table of Bhn VeJ5US tooth numbers,aprefuninary estimate of the tooth numberis established (Table 2). This step in turnleads to determination of a trial value forthe pinion pitch diameter (d).

Afterdeterntining the pitch diameter, aprelimmary sizing of the gear can beundertaken by means of the Q-factormethod ,.Ill The Q-factor method is onewheE'eby the power, speed, and gear trainratio of the gear set are allcembined intoa single nondimensional value (Q), Thisnumber is representative ,of the "size" ofth - load the gear has Ito,support, The Q-

Factor is defined by the form.ula:m evatluated. The facew:idth 'can now becalculated using the formula: n,ll

Q ... HP" (m + 1)

n * m - 3150~)"QF----...::;.K ~C2

wherewhere

m .~ gear reduction (speed ratio)'HP = horsepowern = pinion rpm

c- center distance (inches)F == face width (inches)K ==, K-factorQ - Q~fadorNote that by knowing the speed ratio,

the i.nitial value of the mating gear pitchdiameter (D) can also be determined, andthe pinion-gearoenter distance (C) can be

At this stage, the face width ischeeked

(continued 071' page 40~

!November IDeeem'berl989 I' I

Systematic Approach to Designing Plasticpur and :e ical Gears

Raymond M. PaquetPlastics Gearing Technology, Inc.

Manchester, CT

Abstract:Plastic gears are being used increasingly in applications, such

as printers, cameras, small household appliances, small powertools .•instruments, timers, counters and various other prod-ucts. Because of the many variables involved, an engineer whodesigns gear trains on an occasional basis may find the designprocess to be somewhat overwhelming. This article outlines asystematic design approach for developing injection moldedplastic spur and helical gears. The use of a,computer programfor designing plastic gears is introduced as an invaluable designtool for solving complex gearing equations.

IntroductionAs one of man's oldest mechanical. devices, gears have been

in use For thousands of years. It is no surprise that design techni-ques, manufacturing procedures and standards have beenestablished based on the commonly available materials of thetime, namely wood and metal. When plastic materials were first:used as gears in the1950fsand 196()fs, it was common to designthem using existing AGMA standards for metal gears. For ex-ample, if a designer was considering trying plastic gears for oneof his applications, he would usuallytake an existing productdrawing specifying steel, change the material to nylon and leavethe gear data intact. There were no standards at the 'time to,guidethe designer to do otherwise. It was also eeonomicaltc considercutting plastic gears with the available stock hobsand cutters.

Today, there are still no official "standards" available, butsome tooth profiles have been developed especially for plasticgears and used successfully in industry. If the injection moldingprocess is utilized, then the designer is free from the constraintsof using stock hobs and cutters. Since special ho bs are requiredregardless, (to compensate for mold shrinkages and EDM sparkgap), the designer might as weI1 ineorporate additional modifica-tions, such as full fillet radius, to optimize the strength of the gearteeth.

The modifications to the gear teeth mentioned in this articleare not new to the gearing industry. Engineers familiar with geardesign will. recognize that the recommended modifications forstrengthening the plastic gear teeth are the same ones specifiedfor heavily loaded metal gears in critical applications.

In summary,this article describes the manufacturing processused to produce plastic gears, and explains inspectionprocedures.

Design of Plastic GearsA designer must considertbe pros and cons of plastic materials

before choosing it as a gear material. The advantages are• relative low cost• resistance to corrosion• reduction in weight (about 15% the we~t of steel)• low inerita., self-lubrication capacity• potential for noise reduction• design freedom. to obtain additional features in one product

such as posts, cams, duster gears, trunnions, palls, sprockets,metal inserts and spring anus

• color coding capability ror fast, error-free assembly,The disadvantages include

• lower strength.' greater thermal expansion / contraction• limited heat resistance• size change with moisture absorption.

COMMON PlASTIC MATERJALS FOR GEARS. Eventhough many new materials have been introduced. in Ithepastdecade, the majority of gear applications still call for acetals andnylons. In special cases, polycarbonates, thermoplasticpolyesters and thermoplastic polyurethanes can also heconsidered. (1.51

Acetal:. Strong, stiff plastic with exceptional dimensional stabilitydue to low moisture absorption, resistance to creep and vibra-tion fatigue; low coefficient of friction; high resistance to abra-sionand chemicals; retains most properties when immersed inhot water; low tendency to stress-crack.Nylo!,,-=Family of resins having outstanding toughness and wearresistance, low coefficient of friction and excdlent electrical pliO-perties and chemical resistance ..Resins are hygroscopic; dimen-sional stability is poorer than that of most other plastics.Polycarbonate: Highest impact resistance of any rigid plastic;excellent stabili.tyand resistance Ito 'creep under load; fairchemical resistance; stress cracks in hydrocarbons; usually usedwith addition of glass fiber einforrcement and PTFE lubricant.Thermoplastic po]yeste!: Excellent dimensional stability, elec-trical properties, toughness and chemical resistance, except tostrong acids or bases; notch sensitive; not suitable for outdooruse or for service inhot water. Material is relatively soft and hasthe pot.ential for tooth damage.Thermoplastic polyurethane: Tough, extremely abrasive and

impart resistant material; good electrical properties and chem.i alresistance. Difficult ito injection mold small parts due to thematerial's elastic properties ..Polyester elastomer: Sound dampening; resistance to flex~fatigueand impact.

ADof the above base materials can be formulated with fillers.,such as glass fibers, for added strength, and PTFE,sili.cone andmolybdenum disulphide for added lubricity.

ESTABLISHING DESIGN GOALS. Arriving at the specifica-tions for the best possible gears given an application is a time-consuming operation when considering the following variables..' Load carrying apacity. Strength equations are used to avoidtooth fracture at the root. They are derived from the Lewis equa-tions for beam strength and have been modified for plastic gearteeth.• Smoothness. The gear mesh should be designed so that bindingwill not occur at extreme environmental conditions.• Quiet continuity of action. Ensure that the contact ratio isgreater than 1.0, preferably 1.2, or simply stated, that at least onetooth is in contact at all times..' Cost. If the gears are to be molded in plastic, the task becomeseven more difficult to handle, especially since there are literallyhundreds of fonnulations from which to choose. Inaddition, theuse ,of non-standard hobs allows the design engineer to considerill larger choice of tooth forms, such as the six listed in Appen-dix A ..Because of all th options open much of the engineerswork must necessarily be a process of substitution and elimina-tion. This process involves numerous calculatiens, some of themquite complex.

SPUR AND HEUCAl GEAR DESIGN - A SYSTEMATICAPPROACH.

:::.:.::::.z:....:::.:;...::::.::=:..:....t::::ar:.:a:::;m:..::e::!t::=:ers~.. The gear train design engineer isfirst required to make a study of all the information about theapplication available to him. such as the power to be transmit-'ted, the ratio required, the speeds involved, the environment inwhich the gears will operate, the life expectancy and the spacein which the gears are to be housed.

"the designer then proceeds to make preliminary choices ofnumbers of teeth. diametral pitch, too th form, type of materialto, be used and spur or helical design.

Determine load carrying capacity. The engineer now pos-sesses all the information required to determine what power thegears can safely transmit. If the answer is too low, th effect ofa coarser diametral pitch, a stronger tooth form, an increasedface width, or plastic having higher allowable design. stresses,singly or in any desired combination, must be investigated. Thefollowing is an example of an equation that can be used tocalculate load capacity. rn

AUTHOR:

RAYMOND M. PAQUU is Engineering MlmRgerat Plastics GearingTechnology, Inc .. Manchester, Cl', responsible for the design of customplastic gears and related components. He receioed his BSME from theUniversi.ty of Connecticut at Storrs and an MBA from the Universityof Htlrtford. He is the author of other articles on plastic gearing and isa member of ASME.

HP = D X F X n X J X Sf X KTX KL126,000 X P X Cs X KR

where:HP = horsepowerD = operating pitch diameterF = effective fa.cewidthn = speed, rpmJ = geometry factor

St = tensile strength of plasticKr = temperature factor/(L = life factorP = diametral pitch, or normal

diametral pitchCs = service factor

KR = factor of safety

H the calculation indicate that the gears would be pushed totheir limits, developing prototype part to perform actual Lifetests would beadv:isable.

Options available to optim~ a. gear mesh. In order to getthe most out of the relatively low tensile strength of plastics, thetooth geometry can be altered several ways to be as strong aspossible.• Fu[J fillet radius modification. The tooth forrn shown in Fig.1has a full fillet radius at the root to eli:minaje sharp comers Ithatcould result in high stress points. This modification can add upto 20% to the tooth strength. Teeth of heavily loaded metalgears are also designed with this feature.• Tip relief modification. Tip relief starting hallway up the ad-dendum should be another modification specified for plasticgears. When a 'tooth deflects under load, it can get in the wayof the oncoming tooth of the mating gear. This can ca use noise,wear and loss of uniform action. Tip relief is added to improvethis situation. (See Fig. 2.)• Elimination of undercut condition. If a standard gear has asmall number of teeth, the lower portion on the tooth will beundercut as illustrated on the left in Fig. 3. This condi.tion isundesirable in that it weakens the tooth, causes wear and in-hibits continuity of action.

To eliminate undercutting, the circular tooth thicknessshould be increased over standard as shown in Fig. 3 on theright.• Balance circular tooth thickness. H the gear t'eeth in a me.h aredesigned at standard, they will be the "weak link" in a powerdrive. The pinion tooth illustrated in Fig. 4 dearly shows the pro-blem. (All dimensions are in inches.)

To design the gear teeth for equal beam strength, it is essen-tial that the thickness at the root be equal, as illustrated in Hg. 5.

With the use of available formulas, the tooth thickness of thepinion was increased from a standard of 0.0491 to 0.0640', andthe gear tooth thickness was decreased from 0.0491 to 0.0480 toget an equal thickness of 0.0660 at the root.

Expansion and error considerations. Once the 'tooth thicknessof each gear has been established, the next step would be thcalculation required to determine the increase in center distanceabove standard to cater to all the factors that couldotherwisecause the gears to bind in operation. The designer considers thefollowing equation:

Fig ..:I.

Fig. 2

.~,:" Tefl + Tef2

2

+ C [(T -70) (COEF1XN1 + COEFzX Nz - COEFH)I, Nl +N2 Nl +N2

+ (MIXNl + MzxN2 _ MH).]+ TIR1+TIR2

Nl +N2 N1+N2 2where:

.:lc = required increase in center distanceTCT 1 ,= maximum total composite tolerance of 1st gearTCT 2 = maximum total composite tolerance of 2nd gear

C = dose meshcenter distanceT = maximum temperature to which gear will be sub-

jected (OF)COEF1 = coefficient of linearthermal expansion of material

of 1st gear (in I in / 0 F)COEFl = coefficient ,oflinear thermal expansion of material

of 2nd gear (in/inJOP)COE~ = coefficient of linear thermal expansion of material

of housing (in/in/OF)Nl = number of teeth in 1st gearN2 = number of teeth in 2nd gearMl = expansion due to moisture pick-up of material of

1st gear (in/in)M2 = expansion due to moisture pick-up of material of

2nd gear (in/in)MH= expansion due to moisture pick-up of material. of

the housing (in / in)TIRI = maximum allowable runout of bearing of Ist gearTIR2 = maximum allowable runout of bearing of 2nd gear

14 Geor Teennology

Fig. 4

13 teeth 6011celit

Fig. 5

The calculations enable the designer to specify tooththicknesses and operational center distance. (1)

Calculate contact ratio. If one of the mating spur gears hasarelatively small number of teeth, it is essential to check thepair's contact ratio, particularly if the gears are plastic. Plastics,in general, have high coefficients of linear thermal expansion.When the expansion differential between the gears and thehousing inwhich they are mounted isgreat, and when the max-imum environmental temperature is high, the center distancerequires a significant amount of increase to prevent binding atthose high temperatures ..However when the same gears latercontract at the lower temperatures, they may be out 'of meshto an extent that the contact ratio becomes less than adquate,

One option available to get around this problem is to use atooth form with longer teeth. (See Appendix A). For continuityof action the contact ratio must never be less than 1.0. It shouldpreferably be at least 1.20.

The variables required to calculate the minimum contactratio are the numbers of teeth for each gear, the diametral pitch,the minimum outside diameters, and the maximum operatingcenter distance. If it is less than adequate, the designer canreview the following available alternatives:• tooth forms with longer teeth,• non-standard diametral pitches

(P = 48.5526, for example),• materials with lower coefficients of linearthermal expansion,• higher quality gears,• tighter center distance tolerances,• changes in the numbers of teeth in the gears,

Establish Drawing Specificatio.ns and Tolerances. The finalstep in designing a gear is preparation of a drawing which liststhe gear data .. It must be specified so that there can be nopossibility of misinterpretation. This may seem obvious, butambiguity in writing gear specifications has often resulted incostly and time-consuming changes to expensive molding dies.Appendix E Illustrates the data that should appear on a draw-ing of a spur gear.

Gear Design ExampleIn this example we will suppose that the design 'engineer is

assigned a project to work on a gear mesh for a special type ofchart recorder.

Where does the engineer begin?What procedure should be followed?How should the analysis be done7for this project the designer has decided to use the step by step

approach described so far. Correctly used, the system will. pro-vide a design for gears having an adequate contact ratio,toothprofiles with no undercut, and sufficient clearance to' insure thatthey will not bind when. subjected to the extremes of the environ-ment in which they will operate ..Furthermore, the design will. bepresented in such a form that there can be no misinterpretationof the engineers requirementseither by the molder of the gearor the inspector responsible for insuring [that the requirementshave been mel.

In other hands this system could well produce designs thatwould differ, but be just as valid.

The following constraints wen! outlined by the manager:• costs to be kept as low as possible• material of housing to be polycarbonatewith 20 % glass fiber• the gears will be subjected toa maximum operating

temperature of 130° Fahrenheit (F)'. ratio required is 2 to 1'. bearings must have a maximum allowable runout of 0,001

inches• load is .Iight; material strength is not a factor.• lHe requirement is 260 hours.• input torque is 4 inch-ounces.•'inputspeed is 50' revolutions pel' minute (rpm).

Begin Analysis(All dimensions are in inches ..)

Step 1. Study of design parameters. Some preliminary assump-tiens need to be made to begin the analysis: 1) material of pinionand gear to be unfilled acetal; 2) spur gears will be used; .3) gearsto have an accuracy equivalent to AGMA Quality No. Q6; 4)start with. the PGT -1 tooth form to take advantage of the fullfillet radius and the tip relief.Step 2. Settle upon the numbers of teeth and diametral pitch ..Given the spa.cing of the housing and the required ratio, thefollowing have been chosen:

PlMON GEARNumber of Teeth 1530'Dtametral Pitch 4848Step 3. Determine the load carrying capacity, Although the loadsare ligh:t. the designerperforms the calculation to determine theload capacity. The requi.r~ tensile strength.of the material wascalculated at 1,900 pounds per square inch (psi) ..Therefore, the

unfitUed acetal witha tensile strength rating of a;pproximatety9,000 psi is a good choice.Step 4. Determine the minimum circular tooth thickness (CIT)at the pitch diameter of the pinion to avoid undercut. Thecalculated minimum CIT = 0.0353. Assign at +0.0Cl0, -0.001tolerance to the pinion CTI.

The preliminary data established so far are shown in Table 1.

Table 1

Number of TeethDiametral PitchPressure AnglePGT Tooth FormStand, Pitch Circle Dia.

PINION1548

.20°PGT~10.3125

GEAR304820°

PGT-10.6250

Outside Diameter 0.3640'0.3610

0.66200..6580

Circular Tooth Thickness(at pitch circulardia.) 0.'0363

0.03530.03100.0300

AGMA Quality No.Max. Total Composite TolMax Tooth~To-Tooth Tol

Q60.(10360.0022

Q60.00360.0020

Step S. Expansion and error considerations (to. detennine theoperating center distance). [f perfect gears could beman.ufac-hired,. the operating center distanre would be 0.4712. However,the thermal expansion ofthe gears, gear runout and bearingrunout must be considered 'to prevent the mesh from binding.The designer has calculated that the center distance must beseparated by 0.0061 to allow for the possible variations in thesystem ..Assuming a tolerance of +0.003, -O.(I(lO, the operatjngcenter distance (OCD) is specified at 0.4773 - 0.4803.

Step 6. Calculate the contact ratio (CR) for the establishedvalues. The following six input variables are used to calculate thecontact ratio .number of teeth Nl 15number of teeth N2 30diametral pitch P 48outside diameter Dol 0.3610"outside diameter 002 0.6580"ope:rating center distance oeD 0.4803H

contact ratio CR 1.01A contact ratio of 1.01 is too low. The designer must now at-

tempt to raise it to 1.20. He knows that the molding departmentwill have no trouble if AGtv1.AQuality No. 7 gears were specifiedinstead of No. 6, sa he decidesto find out what improvement thischange might eHect. The maximum total composite tolerano@isnow .0026 for both the pinion and gear, Asa consequence, themaximum operating center distance is reduced fmm 0.4803 to0.4793.

operating center distance OCDcontact ratio CR 1.05

He now tries the eHect of reducing the operating center

NovemberjDec,ember 1989 15

distance tolerance from +0.003, -0.000 to +0.001, -0.000.

operating center distance OCD 0.4773"

CRcontact ratio 1.13He tries even more accurate gears - AGMA Quality No ..8,

having maximum total composite tolerances of 0.0018.

operating center distance oeD 0.4765"

CRcontact ratio 1.16

At this point, he decides to return to the beginning and deter-mine what contact ratio he can achieve by switching the plastiche had first chosen from an acetal having a coeHicient of linearthermal expansion of6.8 x 10-5 in./in.ldeg. F, to a glass-filledvariety having a coefficient of 1.S x 10..5 in.lin.ldeg. F. Theoperating center distance is now 0.4845-0.4855.

operating center distance OCD 0.4750"

contact CR 1.23

The designer has reached his goal, but only by switching toa more costly plastic, and has reduced the center distancetolerance to. less than is desirable.

But he still has another option open. He can use a tooth formhaving a longer addendum. One such tooth form used suc-cessfully in plastics gearing is the tooth form with an addendumof 1.35/P shown in Appendix A. This tooth form will add littleto the overall tool cost.

Gear GrindingSpecialistsR'eishauer RZ' 300:E

Electroni:caUy Cont,r'oUed Gear GrindersCommercial & Preoision Gear Manufacturing!to AGiMA.Class 15 including ....

• Spur - Grinding 1012·112"Diameter• Helical • Hobbing to 24" Diameter• Internal _ 0.0. and I.D. Grinding,• PumpGears Gear Honing w/Crowning,_ Splinesand ,Pulleys Broaching, Keyseating,• Serrations Turning and Milling,.Tooth• Sprockets Chamfering.and Rounding

Suppli.edcompJete to printFinishing operations on YOllr blanks

Grind teeth only

CIRCLE A·7 ON READER REPLYCARD

JI 6 Gear fechnology

To eliminate undercut, the pinion will now be required to havea circular tooth thickness of 0.00424 - 0.0434. The minimumoutside diameters of the pinion and gear will be 0.3796 and0.6725, respectively. Returning to the cheaper unfilled aceta], a.center distance tolerance of + 0.003, - 0.000 and AGMA Qual-ity No.7 gears, the designer tries again. The maximum centerdistance is now 0.4882

outside diameteroutside diameteroperating center distance

Dol002

OeD0.3796"0.6725"0.4882"

contact ratio CR 1.20

Step 7. Check the load carrying capacity. Even though the loadsin this application are light, the designer checks the allowablehorsepower to determine what difference the new tooth f.orm h<16made. If any change to the gear design is necessitated, it willamount to no more than a slight increase to the face width.Step B. Establish manufacturing and inspection data. Finally, thedesigner arrives at the manufacturing and inspection data. to goon the production drawings. The complete data for the IS-toothand 3D-tooth gears used in this example are shown in Appen-dix E,

Manulacturing of Plastic GearsDescription of Molding Dies and the Injection Molding Pro-

cess. A molded gear, of course, can be no more accurate that themolding die which produces it. Basic considerations for gearmolding dies are the same as for any precision molded product.Since molded gears an'! usually smail in relation to the size ofaverage moldings, they lend themselves admirably to beingmolded in small, high speed automatic injection mal dingmachines (20- 80 ton range). This allows .for compact dies,usually with one to eight cavities.

Several factors can be built in to a molding die to produce themost accurate gear possible.• The increased strength of case-hardened die frames will enablethem to withstand the abuses of the molding process and canmaintain their accuracy throughout extended useful life.• The elimination of wear bushings allowed by hardened steelsurfaces in the bores removes the additional errors resulting fromless than perfect concentricity of these items.• The mold should have a balanced runner system to provideequal pressure drops into all cavities.• Adequate venting in the cavities will allow air to be displac-ed by the flow of the plastic.• Adequate ejection systems ensure minimum distortion of theproduct when ejected from the die.• Adequate interlocks between the die halves remove themisalignment of running fits provided in the guide system.

Figs..6 and 7 are cross sections of a gear molding die.VVhenthe molding die is closed, the melted plastic resin is in-

jected under high. pressure into the gearcaviti~. When the resinsolidifies, the molding die opens, and the plastic gear is ejectedfrom the die. Cycle times usually range from 10 to 30 seconds,depending on the part geometry and the plastic resin used.

Several factors in a molding die can contribute to the gear'srunout:

Gear Tool S,peclallsts3601 WEST TOUH'Y .AVENUE.

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1-80'0'1.'628-2220 In IIIL. '-800'-628-222.1

GEAR TRAINING PROGRAM1. BASIC FUNDAMENTALS

1. GHr HI.toryA. CycIOldal TeethB. Involute TeethC, Gea, Cultlng MachmesD, Gear Cutting Tools

2. GHr TypesA, Parlillel AxisB Intersecting AxisC Skew AxiS

3. GHt Rittos.., Involute OUr Geometry

A. Nomenclature'8, Involutometry - Contract Ralio. etc,C, Helical Gears - lead - Helical Overlap

5. OMr Tooth Sy__A. Full DepthB. Full FillelC, Slub Depth

S. ~IFonnu~7. M~ - (I.T.W, Trig Book)

2. HI SPEED STEELSA, Common TypesB, Special TypesC. Heat Treatment - MetallurgyD, ControlsE, Surface TreatmentsF, Special Cases

3. CUTTING THE GEAR1, Forming

A. MillingB. BroaehongC, Shear Cutting

2. OenedtIngA, Shaping

al Rack Typeb) Circular Typec) Machine Types and Manufar:turers

d) Schematic - PrinCiplese) Speeds- Feedsf) Maehine Cutting Conditions

B. Hobbingal The !-lobbing Maehineb) Types and ManufacturMSc) Schematie - Differential and

Non-Differentiald) Speeds - Feedse) Climb Cut - Conventional Cutf) Shifting - Types

3. Th. Hob .. I Cutting ToolA, How II CulsB, Tolerances and ClassesC. Multiple ThreadsD. Hob Sharpening and ControlE. The Effect of Hob and Mounting Errors

on the Gear... The Shaper CUtter .. e Cutting Tool

A. K/:Iow Your Shaper CuttersB. Design UmltationsC. SharpeningD, The Effect 01Cutter Mounting and

Errors on !he GearE. Manufacturing Methods

5. Tool Tol~nc. Va. GHt TolerlnceA, Maehining TolerancasB, Gear Blank Aeeuracy and Design

limitations

4. FINISHING THE GEAR1. Gur FInishing - Befor. Hlrdenlng

A, Shavinga\ The Shaving Cutterb Types of Shaving - Conventional,

Underpass. Diagonalcl Crown Shavingd) Shaving Cutter Modificationse) Co-ordinaling Tool Design-

The Shaver and Pre-Shave Tool1) R&-Sharpeningg) Maehines

a Rolling2. GHr Finishing aft ... Hat Treat

A. Honinga ~ingC, Gnndlng

a) Methods - Formed Wheel-Generating - Threaded Wheel

b) Maehme Types

5. GEAR INSPECTION1. Functionll

A. Gear RollersB. Gear Charters

a! Reading the Chartb Tooth-to-Tooth Composite Errorc Totsl Composite Error

C, Master Gearsa) Tolerancesb) Designse) Speda! Typel

2. AntIIytIcaIA, Sfze - Tooth Thicknesse. AunoutC, SpaeingD, lead -E, Involute

3. Automatic Ind hml-AutomatlcA How They WorkB, Whal Can Be CheekedC. How Fast

... Chlrt Interpret.tton - AnIIlytieal Mel FImClIonaIA. Reading the ChartsB. Which Errors Affect Other ElementsC, How 10Correel the Error lhe Chart SI'IOwa

8. INDIVIDUAL INSTRUCTIONAND SPECIFIC PROBLEMSOR PLANT TOURThis Program Is tlexlble and changed to mae! theneeds of each group.

The 4-day program consists of a coordinated series 01 lecturee given by the Engineering,Production and Inspection staffs of Illinois Tool Works Inc, They represent over sixty years ofexperience in gear and tool specialization.

The sessions are conducted with a technique and approach that leads to Intereslngdiscussion and participatiOn. Starting with the basic: fundamentals, the program Is directedInto those areas of greatesl interest and value to the people attending the particular session.The groups are kept small so that this object is readily accomplished.

AI mentioned, the planned program lasts lour days. OnHalf of the fourth day is for In-dividual diSCUHlon 01 specific problems In a detailed manner with members of the illinoisTool Works' staff,

More than 4,000 individuals !rom hundreds of companies representing manufacturing.engineering, inspection and management. have come to Chicago for these programs, Theyhave been conducted on a monthly basiS since 1958, ClU18S have also been conducted inEurope, We are certain It\althiS well rounded program has helped all of them to a bener lOband aIIo given them a better understanding of engineering. manufacturing and inspection.

All thoM attending are assigned to the same hoIeI. This promotes friendly contact anddiscussion of mutual problems and Interesls. Tuition lor the course includes transponationfrom the holel to ITW and back. one group dinner. all eontlnental breakfasts and all lunches.

We hope we may include your company in one of our Training Programs. _CIRCLE A-8 ON READER REPLYCARD

ITW ILLINOIS TOOLSA Division of illinois Tool. Won. Inc.

1990 GEAR TRAINING PROGRAMFour D.y Seminara

JanuaryFebruaryMarchAplll

,7·20,50,112·15U

MBYJuneJulyAuguII

15-'812·'512·159-12

14-17,,.,4, ,11-111

13-18

TUITIONFEE: 11110.00NOTEI AddItIoMI atudenIII. _ -..nY. _ ... Il00.00

Includes the "anspor1lllOn from lhe /'IoIeI1o ITW PC! ~, or.- VOIJP dlnMr.hoIpIIallly fMebng. COO",*,I8I bruk1_. PC! .. lullCMl

The SocIety 01 ManulllClunng Engo.-'l (S MEl l1li IIIIP'1MCI '" Sc;hooI 10<Prol_8I Credits \OWItd lhe S M E ~oon f>rogrMI CtedIIs ... _,_

on lhe bull 01 OM credit 1* COOIenihOurFw BIIItIIfIoMI ~~ -act:

I'IOIIERT H. IIODDOW.....,.TNInIng708-675-2100'-I00-4I21-2220

tn IL Call: 1·1OQ.821-.2221

Fig. 6 Die Open Fig. 7 Die Closed

• The .OOOl/.(!()(I2" running fit required between thecore pin andthe stationary half of the die;• An additional .(!()(Ilto. .0002." running fit will be present ifsleeve ejection is required aroundthe core pin. because the solidanchor is lost;'. Because the gear cavities themselves are a.series of concentricrings, the potential for runout error exists ..• Uneven plastic flow resu1tifl8 from the off-oenter gating posi-tion on the part will introduce additional runout in the gear ...

The selection of a molder should be given. careful considera-tion. True, given a correctly designed and accurately mademolding die, any competent molder caJl. produce gears;however, not all molding companies can be classified as gearmanufacturers.

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iBooth 236CIRCLE A~9 ON READER REPLYCARD

~8 Gear Tec:hno~logv

A good plastic gear manufacturer should have the followingcapabilities:• expenenee in molding a.wide range of gears;• ability to advise on product design andseleetion of materials;• availability of molding presses most suitable for gear molding;• availability of inspection equipment necessary to maintain

proper quality control (such as gear checking equipment) ..Gear Cavities ..P,opuiar wisdom holds that molded gears are

not as accurate as machined gears, This is inaccurate. A moldedgear held to the tolerance of A:GMA Quality Number Q8is justas accurate as a machined gear of the same quality number. Itis true that gears have not yet been molded Itothe highest preei-sion obtainable by machining, but the number of gears requir-ing such precision represent only a small percentage of all gearsmade. In general, plastic gearsa:re usually specified AGMAquality Q6 or 07.

The idea that molded plastic gears need not be as accurate asmetal gears is based upon the contention that, because of theyielding nature of plastic, runoutand tooth-to-tooth errors do.not have the same illef£ects. This is incorrect because plastic gearteeth that are flexing to an excessive degree because of inac-curacies will fail through .fatigue and wear much earlier th~ ac-curate teeth,

All plastics shrink when changing from a molten to a solidstate. As 3. consequence, all mold cavities must be made largerthan. the product specificatio.n. For example, ifa. molded gear isto have an outside diameter of 1.200', and the plastic has a moldshrinkage of .025 inI in, then 'the outside diameter of the cavitywill be required to be 1.2308R

•

Inmakinga. gear cavity, however, it is not sufficient to. takea generating hob and machine an oversize gear. Compensation

1----'.I \

I \i

IIIt,, .

" .

STADAR.D GEAR

--~

STANDARD GEAR

~~MOlDED GEAR

\

Flg.8"

must also be made for the pressure angle of 'the hob. If it isn't,the result will be a.molded. gear with a serious profile error . h willhave a.larger than aoooptable tooth-to-tooth error. For example.in Fig. Sa an enlargement of a32 D.P., 20 degree P.A., gear toothis shown, and superimposed upon it is the profile of an 'oversize~toothcutwithastandard32D.P., 2OdegreeP.A. hob. FI8..ab shows the standard gear tooth. and this time superimposedupon it is Ithe pr~file of the moMed tooth (after shrinkage) thatwould be obtained fromthe oversize 'cavity.

Note that the tooth ,of the molded gear departs ,considerablyfrom standard. It is thicker at the root and thinner at the tip. (Ithas a pressure angle much in. excess of 20° .)

The form.ula used to calculate the correct pressure angle is:

where:D == Pitch dOCLediametertPl = Pressureangle ,of hobtP]; Pressure .angleof molded gearS, "'" Shrinkage

The Iteeth in the ,cavity must be ,caJ'efuIly compensated forshrinkage so that., when the molded gear solidifies and becomesstab1e, Ithe teeth will have the correct profile. This design workis further complicated. in the case of the helteal gear, because 'theaxial shrinkage is usually different from the shrinkage acrossthe diameter,

Compensating correctly for shrinkage in a gear requires that'the mold designer have a. thorough understanding of geargeometery, plus censiderable experience in the shrinkage

I

ON REVOLUTIO OF GEAR-tFig.lO

behavior oEal[ types and grades of plastics.The actual manufacture of accurategear ca.vi.ties is ac-

complished by using eerreentienal or wire EDM machines.

Inspection .of Plastic GearsOne practical method of checking gear accuracy is Ito,rota te

the manufactur~d gear in dose mesh w:ith a.master-gear usinga center distance measlllri~g instrument. The model shown inFig. 9 is equipped with a dial indicator ,and requires that theoperator note the radialdisplacements as the'gear is rotatedmanually through one complete revo~uti.on.

The more sophisticated models trace the radial displacem ntson a moving chart (See Fig, 10'.) ttwough an eleetrentcdevlee.

The errors present in a gear are runout, lateral runout (wob-ble), pitch error, and profile error.

The pitch 'error plus Ithe profile error add up' to the tooth-to-tooth composite error, and thls, plus the totall runout, is known

(continued on page 23)

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CIROLE A-lO 0l'1li READER REPLY CARDINovember/December 1989 19'

EDITORIAL(continued from page 5)

area alone, and we have no reason tothink the situation is much betteranywhere else in the country or that itwill improve in the near future,

I'm not sure how we got to this placein our thinking about work ..for myfather's generation, high school was theend of the educational line for mostpeople. Many were unable to remain inschool even that long. Those whoqualified for skilled apprenticeship pro-grams in the "trades" were to be envied.No one thought that a young man orwoman learning a skill that would pro-vide economic security for a lifetimemight be a 'failure" because that skillwas acquired on the job instead of onthe college campus. "Trades" were not

job vital to our economy requi res fouryears of college ..And, cootrarv to popu-lar opinion, college does not providethe advanced training necessary toqualify for many highly skilled jobs.Furthermore, I'ack of interest in thetraditional scholarly and professionaltraining that colleges provide best doesnot make for a "second-class"employee.

But that's not the message we giveour young people.

In the meantime, the metal workingindustries are short some 1500 workersevery year in the Chicago metropolitan

CIRCLE A·n ON READER REPLY CA'RO20 'Gear Technology

thought of as second choices for peo-ple too poor or unambitious to go tocollege, They were honest jobs requir-ing just as much hard work and trainingas any other. No one was embarrassedto say, "I'm a precision gear maker."

These jobs haven't changed. Theystill require intelligence and' hard work ..They are demanding and challenging;they provide a decent living and plentyof opportu nity for advancement. Noone need's to be embarrassed to admitto working in a gear shop.

It's our thinking on the subject that'schanged. Because precision m eta IIworking or gear manufacturing are notnecessarily "glamorous" or "profes-sional," the highly qualified young peo-ple who might enter these jobs are notencouraged to even consider them.Maybe if somebody did a.t.v. seriescalled "LA Gear Cutting' and cast itwith beautiful people in tailor-madecoveralls, the job would be moreappealing.

A more practical suggestion is tobegin with our own attitudes ..Those ofus familiar with the gear business,whether we are managers, foremen, oroperators, can encourage the youngpeople we know to consider thepossibilities of entering a "trade." Wecan inform them of the realities of workin skilled jobs like gear manufacturing:That during the last 40 years the U.S.has never been able to produceenough qualified precision metalworkers to filii industry need's; that thesejobs can pay as much as $35,000 to$50,000 a year; that even during theirfirst year of training, precision metalworking apprentices can expect to earnnearly $20,000 annually, that training isusually subsidized by the employers;that at age 26, a young tool and diemaker can earn about $40,000 in con-trast to the mechanical engineer of thesame age, who willi' earn around$35,000.

Ta'ik to the guidance counselors atyour local schools. Do they know thesefacts? What are their attitudes aboutnon-college job opportunities? Do theyconsider such careers "second-class"choices? Are they aware of the jobsavailable locally in gear manufacturing?Do our high schools provide any kind

(continued on page 22)

EDITORIAL(continued from page 20)

school guidance counselors.We can beoome involved in the ef-

forts of local communitycol'leges,many of whom are in the forefront ofproviding advanced manufacturingtraining. Wmking ,in conjunction withlocal industries, these colleges are pro-viding classes, not for degree programs,but to support and supplement the on-the-job training that local manufac-turers provide. Such school programscan be life-savers ~or the medium-to-small! manufacturer who does not have

of shop education that might begin tosteer qualified young people towardthe skilled trades we desperately need?

We can also recruit capable youngpeople to our own training programs.We can encourage organizations likethe Tooling and Manufacturing Associa-tion, which has a program that activelyworks to spread the word about skilledprecision metal working jobs to high

Just"averate"

doesn'tcut

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We're organized to gel you Ihegear generating 100Is you need -wh«m you nfHild them

Our pncesare surprisinglycompe1ltive and we are aN·eringan ·expandedillne· of oN"lhe-sheR'standard gear tools.

Fa8I respon!le 1o yourengin"red s,peclal and prQIQ..type needs.

OUf,producm, which havecontinued: 10 !let the qualitysta..".

dard lor the Industry for moreIh!!!170 yea"" ·are )QUI ~r·anee 01 reliable, durable, highperformance hobs, shaper cut-ters, master gears and wonngea.r'hobs.

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gesr tooUng. Just call, TOLLIFREE,'~2220(lnllilinois, call1.aoo.El2.II-2221).

Our widely aoclaimed GearSchOOl also contlrlu8sIo klMpAmerk;a's gear !!!!:hnolQglsts up10dale on Ihe state-or-the-art ingear making and gearlnspectlon.

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CilRCLE A-13 ON READERREP,lY CARD.22 Gear Tecnnology

the resources to provide an elaboratetraining program of his own. The offerof used machinery or time and exper-tise to such programs can help begin toclose the gap between our need fortrained workers and their availability ..Discussicns with school administratorsabout the need for such programs canbean important first step,

Those thousands of vacancies that gounfilled every year are vital to the suc-cess of our industry. Every year they re-main vacant weakens our competitiveposition. It is not enough to complainabout "inadequate training" or an "un-skill'ed work force." We have a respon-sibility to get out the word about theopportunities lin our field. We knowthat, farfrom being "second-rate", theskilled workers on our shop floors aretalented specialistsessential to the sur-vival of our businesses. We have to letthe rest of the world know that too.

Ex.ceUence in gear rnanutacturmg isas important to our societyas excel-lence in either plumbing or phiilosophy.If we allow gearing jobs to go unfilledbecause of some mistaken notion thatthey are "humble" or not worthwhile,not only will both our pipes and ourtheories fail to hold water, but ourmachinery, our businesses, and oureconomy will also suffer. Ultimately, itwilli be our society that ends up as"second-class",

SYSTEMATIC APPROACH ...{continued from page 19)

as the total composite error ..As mentioned. previously, the AGMA quality number is used.

to classify the q-:-ualityofmetal gears as well as plastic gears. Thenumber specifies the gear accuracy in terms of maximum tooth-to-tooth and total composite tolerances allowed. The AGMAquality numbers and the corresponding maximum tolerances arelisted in. the AGMA "Gear Manual 390.03".

SummaryThe injection molding process allows the gear designer to free-

ly modify Ithetooth profi1eto obtain maxim.umtooth strength.These modificatio·ns will add little to the .finaltoolingc,ast.

The gear design example was chosen to point out the manyvariables involved when designing plastic gears. The use of asystematic design approach allows the overall design problemto be broken down into smaller blocks which can be analyzedindividually. Given another des~gn with different constraints(fixed operating center distance, for example), the sequenoe ofevents in the design prooess would differ, but 'the problem woul.dstill be broken down into smaller blocks and analyzed one stepat at time.

Correctly used, the systematic .approa.ch will provide a designfor plastic gears having load canying capacity, adequate contact,as close 'to balance tooth thickness as possible, and sufficientclearance so that no binding will occur at the extreme operatingconditions.

APPENDICESAppendix A - T,ooth Forms for Plastic Gears.

(PCT"'l'OOT1l FOIIM)

(continued .on page 26)

'GEAR DESI'GNI SEMINARWith Computer Applications:

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Sponsored by: The Department of IndustrialTechnology

University of Northern Iowa

For further informatian. contact:Canferences &. Visitor ServicesUniversity af Northern liowa242 GilchristCedar Falls. IIA.50614-0029(319) 273-6899

CIRClE A·14 'ON REA10ERREPLYCAIU)'November/December 1989' 23

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The W800CNC Gea,r G,rinder (Wiener System)With leading edge technology, the W800CNC becomesthe universall Spir,allBev,el Gear Igrinder for any geargeometry. Perfect for ,ground gear quality app'licationsup to 3,1.5" 0.10., the grinder offers great versatility,short set-ups and superior accuracy.

The PNe :Se:ries Gear Check'e:rsCompact, new CNG corrtroued gear checkers providefu'lly automatic measurilng: of gealfs up to 80"' 0.0. Fastoperation, hliglhaccuracy, exceUent documentation anda.wide v,al'lietyof software modules, form the perfectgearcl1ecking package.

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SYSTEMATIC APPROACH ... (continued from page 23)

(ISO 53-1974 (E) Tooth Form)

FIGURE - R.pruenution of til., pr,of,il, ofmodul., m = 11or'of diam.tr ..1 pitch P <= 1

(AGMA Tooth Form)

Addendum

2P

Coars&oPilch Fin&oPftch19.99 aJld Coarse_r 20.00 and Finer

1.000 1.000P P

1.250P

1.20 . 002pT.Dedendym

2.250--p 2.20 + 002'P .Whole Depth

Circular ToothTrl.ickness

'I'

2Pp .. [)Iemalra! Pitch

Appendix B - Computer Software.,U the design engineer has a personal. computer and a gear soft-

wave program, the time involved in designing a train of gears isreduced from many hours to a matter of minutes. It can proveto be an invaluable tool for a designer who wants to try manyoptions in obtaining optimal gear meshes. Appendices B, C, andDdescribe one of the commercially available software programsfor plastic gears.

Because mathematical and interpolation errors are eliminated,the designer is free to spend more time designing gears and lesstime solving mathematical equations.

Summary of Computer Program Features(6)1) Program runs on IBM PCsand compatibles.2) Design. can be for either a spur or helical gear.3) Designer can choose either English or Metric Units.4) One gear can be designed alone, or two meshing gears can be

designed simultaneously.S) Gear data can be saved, retrieved, printed or deleted.6) When an input value is entered in one of the sub-program

selections, it is also entered in the remaining sub-programs,For example, if the diametral pitch of 48 is entered in sub-program "A", the user does not have to enter it again in sub-program "G"; it is already displayed there.

7) Thecalcula.tions in the program have been designed similartoa spr-eadsheet. The user can enact "what if' variations bychanging input values. The output values are immediatelyr-ecalculatedand displayed.The program is a series of sub-programs which perform

various calculations used in the process of designing spur andhelical gears. (See Appendix C for a listLng of the 12 sub-programs available in the 'Main Menu"). Recognizable descrip-tions and symbols are employed throughout the program. Theoperational. procedure can be mastered in less than an hour.

A Complete Une of

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CIRCLE A~16 ON READER R.EPlY CARD26 'Gear Technology

Appendix C- Main Menu.Saeen

A: SML1ST,(dsk) (gr #1)1

SME SOrT(gr #2)1

English Spur(unit) ,(type)

Model INew

IPlastics 'Gearing Technology, line. - Gear Design IlProgram... • "Main Menu"· Of ..

Aj Oper Phi, standi t,sIand a, ht, andl POIB) Outside dia, root djJa.andi Oomax ,(given t)C) Minimum circular tooth thickness to avoid undercuttingD) Circular tooth thicknesses, for balanced tooth strengthsE) CMOD. minimum o,P9mtingl center distanceF) 10eilaCG) t1 +t2H) Contac~. ratio, FlA, AA, 0/oFlAI) Gear testing radius ,(min and max)

J), Measurement 'over pins (min ,an.dlmax)11q, Horsepower ratingsq Cheek and10r Iprint gear data. specirfied on ,drawing

M), Exit

F2Enter menu selection -» 1M

IF1 He'l,p' Ty-pe Fa Mode' F4 IF5Unit Man Disk

10ifSwap

F6 10'1 F7 New 'fe Clr1 rs IRet1l FlO' Sav1102 Del CIr2 Ret2' Sav2

Description of abbrevationsused in the above Main Menu

Qper Phi, operating pressure ,anglestand t standard circulas tooth thicknessstand a standard addendumht , whole depthPD " .. , .pitch diameterDomax , . maximum allowable outside diametert circular tooth thickness

C:

OvfCD , close mesh center distanceDelta C . . . , , , required. increase in center distancetl + t2 , ., sumo! the tooththiclmesses for a given OACDRA , , , , , ,rnc:ess actionAA , , , approacnaction%RA . . . , . . . . . . . , . percent recess action

Appendix.D - Examp e of a Sub--program Screen ,(for Contact Ratio Cakulatlon).(6)

SME1:5T SME 30T English Spur Mode 1 Calc lPage,11of1

PalfRmeter IDescf,iptionContact. ,ratio, RA,. M" OIORA

Symboll Gr#number of teethnumber ,of teethdiametral pitcholllside diameteroutside diameteroperating center distance

iN 1IN 2IPDo 100 2

OeD!RAAACR

%RA

Vallie Units1530

48.00000.3796 inches:0','6,125 lnches0.4882: incnes0.050110,0,235

1.19668.111

Fl

recess action,approach actioncontact ratio'percent recess action

User iNote:'Gear 11 ts tile drive geaJl',andGear 2 listhe driven 'gear.

HelpEq,ua

F2 Fa Mode F4 Calc F5 10ir F,IS, 11011Man Swap 1011

IlPgU,p'PgOn

Prrev page' lEse ExitINexlPage

Appendix E - Manufacturing and Iaspection DataFor The Pinion. and GeM

PIN]ONDATA

Basic Specifications

number of teethdiametral pitchpressure anglestandard pitch diameterPGT tooth formstandard addendumstandard whole deptheire tooth thickness max at peDeire tooth thickness min at peD

Manufacturing and Inspection

1548.0000

20.00°0.3125"

40.0281"0.0631"

0.04340"0.04240"

I

,

gear testing radius maxgear testing radius minAGMA quality numbermax total composite tol of gearmax tooth-to-tooth camp tolerancenumber of teeth in master geareire tooth thickness of master geartesting pressurediameter of measuring pinsmeasurement over two pins (max)measurement over two pins (min)max allowable outside diameteroutside diameter tol (+ tal)outside diameter tol (- tol)max root diameter

0.1716"0.1677"

Q70.0026"0'.0016"

960.03270"

8.00z0.0400"0.3920"0.3903"0.3826"0.00001'

0.0030"0.2718"

Engineering References

mating gear part numbernumber of teeth in mating gearmax operating center distancemin operating center distance

30Tgear30

0 ..4882"0.4852"

GEAR DATA

Basic Specifications

number of teethdiarnetral pitchpressure anglestandard pitch diameterPGT tooth formstandard addendumstandard whole deptheire tooth thickness max at peDeire tooth thickness min at peD

3048.0001.)

20.00°0.6250"

40.0281"0.063r

0.03100"0 ..03()(X)I'

Manufacturing and Inspection

gear testing ramus maxgear testing radius minAGMA quality numbermax total composite tol of gearmax tooth-to-tooth comp tolerancenumber of teeth in master geareire tooth thickness of master geartesting pressurediameter of measuring pinsmeasurement over two pins (max)measurement over two pins (min)outside diameteroutside diameter tol (+ tol)outside diameter tol (- tol)max root diameter

0.3114"0.3074"

Q70.0026"0 ..0014"

960.03270"

8..00z0.0400"0.6851"0.6828"0.6765"0.0000"0.0040"0.5503"

Engineering References

1ST GEARIS

0 ..4882ll0.4852"

mating gear part numbernumber of teeth in mating gearmax operating center distancemin operating center distance

References1. McKINlAY WILLIAM &. SAMUEL PIERSON. Plastic Gearing

Technical Manual. ABA/PGT Publishing, Manchester, CT.1976.

2. AGMA Gear Handbook (390.03 Volume I) AGMA,Washington, D.C.

3. DuPol'ltDelrin Design Handbook. E.!. DuPont De Nemours &Co.. Polymer Products Dept., Wilmington, DL.

4. DUDLEY, DARLE. Handbook of Practical Gear Design.McGraw-Hili Inc., New York, NY. 1984.

5. ADAMS, CUFFORD E. PlasHcs Gearing: Selection and Applica-

28 GeorTechnology

tion. Marcel Decker Inc., New York, NY. 1986.

6, PAQUET, RAYMOND M. & PAUL DZILENSKI Plastic Gear-ing Software Program. ABA/PGT Publishing, Manchester,CT. 1987.

Acknowledgements: Presented at the SME Gear Processing andManufacturing Clinic, November 1-3. 1988, and at the American GearManufacturers Association 17th Annual Gear Manufacturing Sym-posium, April 9~11, 1989'. Reprinted with permission of bothorgtmizations.

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Hard Finishing and Finefinishing Part 2

Dr ...-Ing, H. SchrieferC. Hurth, Munich, West Germany

EdUots Note:. Part I of this article dealing with the geometryof gear flanks, kinematics, and drive systems, tools, and com-puter assistance for hard and fine finishing, appeared in our lastissue.

Operating Sequeaoes andMachining Results

F~.1shows the possible operating sequences for fine finishingand for hard finishing, integrated into the traditienal sequences.It dearly foHows from this table that the aims of fine finishingdiffer from those of hard finishing.

Fig. 1-Operating sequences for fine finishing and for hard finishing.

AUTHOR:

Dr. -ING. HERBERT SCHR1EfER is with Hunh Company,Munich, where he .is technical numager for the Division of Machines andSystems. He studied at the Technische Universitiit in Berlin and workedat the Laboratory for Machine Tools (WZL) at the TechnischeHochschule .Aachen where he developed the geometry and kinematicpart of a program sequence for bevel and hypoid gears. This programsystem represents the moste:xtenslue and universal computer analysisof the run ning and stress conditions of complex gear drives today.

30 'Geor Technology

After shaping or hobbing, the tooth Hanks must be eitherchamfered or deburred, Here it is paramount that the secondaryburr produced will not be formed into the flank, but to the faceof the gear, because during hardening, the secondary burr willstraighten up and, due to its extreme hardness, will lead to ex-cessivetool wear.

It ischaract.eristic of all further operating sequencesrepresented that the tooth gearings produced are ready for im-mediate assembly. VVhich of the operating sequences shown isoptLmaJ will depend on the quality required, on economic con-siderationaand on thedrcumstanees of the sequencesavailable.

Now we wiJl show some examples of fine finishing and hardfinishLng. Along with conventional evaluations using themeasurements of profiles, tooth traces, and pitch, statisticalevaluations will be made to document the wtiform output Tothis end, workpiroesare taken from manufacturing lines, and theresults of profile and tooth trace measurements are plotted byusing a point of reference. Thus, broom diagrams, whose rangeof tolerance is limited by preset windows, are set up. further'evaluations are obtained by means of the double flank total com-posite error test and by noise measurements.

Results of fine finishing are shown. in fig ...2. Damages shownon the double flank total composite error diagram have beenremoved, and a distinct reduction on the broom diagrams canbe seen ..

After removing the damages and improving the flankgeometry I fine finishing is followed by a.marked reduction of thegenerated noise.

Noise analysesare carried out man unloaded condition. Noiseemissions of car gear transmissions are particularly annoying inthe lower load range, since they tend to override those of theengine.

As you will note in fig. 1, another aim of fine finishing is todispense with the noise test and the manual removal of damagesafter hardening of shaved or rolled gears. This maybe illustratedby a hard tinishing mode where work gears occur with damagesat the flank sides of up to 3S0.um. The task is essentially toremove the defects in the marginalarea of the flanks, while tak-ing into account relatively large admissible radial. deviations andwobbling ofthe gears, On a typical customer sample this pro-cedure resulted in a tool life of a finishing tool in excess 018000parts and a. cycle time of about 15 seconds per part, A con-siderable optimization at quality and cost for finished gears in.mass production can be reached because of low production costs~orgIleenshaving or rolling, the elimination of the noise test andremoval of detects, and the little ,effort required for fine finishing.The use of simple work conveyors also' contributes to higherquality and lower costs, although these conveyors are not en-tirely safe from causing damage themselves.

An indispensable prerequisite is, however, that the heat treat-ment will not lead to excessive incalculable variations of thetooth geometry.

The fine finishjng process also resulted in the percentageofgear boxes returned for reassembly dropping to a range of 0.3per thousand, though the fine finishing was not followed by a.noise test. The reason is that manual removal of defects involvesmany subjective imponderabilities, while fine finishing ensuresthat even the slightest damages will be definitely removed.

Inadmissible deviations of the teeth after hardening, such as

L£AD';;-~ -----:-- -=;-::;'i.; ;1 .~- ' .!.' '. ~. '; .~. ..t .' • .. .· .. ..I. ,

• r •••.. . ,..... ... , .." .· ....· .· . ... . .. '" .. .. : ~.. _ -..... .

Rg. 2 -Working example ,offine finishing a gear.

bent teeth, need, however, to be removed before fine finjshingby means ofan automatic two-flank rolling test.

Fig. 3 shows the macrogeometrical results before and aft.erhard finishingw:ith a CBN-()oated tool. It can be seen that hardfinishing will produce an entirely definite geometry ,of toothflanks.

The desired gear flank has a slight profile bearing and facecrowning, and it has been slightly modified at the addendumarea ...In this case, a stock removal per flank of 50JU11will besufficient.

Sinceany~y accurate hard machining process is alwaysthe most complicajedand costly operation in the work .flow ofgear production, this production step should not be used in im-proper extension. A minimization of the required stock removalfrom the hardened Hank is also appropriate for the necessarycase-depth {1I10th mm of case-depth thickness will require acementation 'time of about one hour} and in view of the reduc-tion of hardness caused by the removal of excessive byers at themarginal areas.

It should be' further noted that, for reasons of load eapacity,the machining s.tep in the root fillet should be as small as possi-ble, or precutling should be carried out with the protuberanceentering tangen'tiatlly into the hard~finished flank,

The aim of minimizing the case depth also results from the re-quirement not to core-harden the synchro mesh gearing nor thetooth tips ·ofaddendum modified teeth with an extremely hightip and, consequently, a minimum thjcknessat the tip.

For the example shown 'lite machining time was 48 seconds.As an average, quality grade 5a.cc. DIN 3962 was obtained. Forthe roughness of 'the flanks we have Rzo 3, !Um,R~ = O.4iS

--- ----

Doubl.-fl.ft"- total compo_ite di.llram~_ '

-::.;;;; ;a;;•• ;;;:;;:.·:: .:~:-;. .••• 4 '1 _., ••••••••......................... ,. - .•:::I:::=:::::;.:::~;:::: : ; . . .

.......................... t ••• .. ••_ _ , •••••• _.. • I............ .. .._ _. . ............ ........... .;:r:::~:::::!::::!:;:::::;!:~::~··::: ...-~.. - ..~ ----....... ..;;;..-;:...;;;;;;:~:;:-:;;:..~.:; :;. ...............-- ~.. .................................... .. . ..................... _ ....................................... ,.~... . .::::::::.; .,-;.....::~..::::::.... .. ..:,-::::::-.::::::::::;;:::e;;.;;: :~:; - . .~ &......................... .. .. .-_ -- - , .EF.;:;~:i!:;r!!;;r=!!:::::!;;:~;::..: ~... :~:.. :

- -- - - - -- - -

·1,,,

Itl, profilerh

Fig. 3 - Profile and lead dj"gr~ms before and ~fte1IiMd fi!lishin,g.

~m. The variation of the measuremen! over flanks is less than20,.an.

Results from hard finishing are presented in Tables 1 and 2together with profile, lead, and pitch measurement records. (SeeFigs. 4-12.)

In the middle of the profile and lead f'ecords the requiredmodificat:ionsa:re given.

INovember/December 1989 31

SE,PELG,EAR GRINDE,R........--------..... igh Production - Accuracy - .Re/iabi/it

MODEL FKP_32~1O IMMEDIA IE DEUVERI,ES

.' MAX. DIA. 13.58" • AUTOMATI'C GRilNDING CYCLES

• D. P. RANGE

• !HELIX ANGLE

48-4 '. FASSLERO..5.A. DRESSING

• PRO:FILEMODIFICATIONS

• WHEEL DIIA. 17.7" • ALLEN BRADUEY PlC

Iinstallations Throughout The US.

Exclusive Import.er Por INorth America

PEELeo MACHINE TOOtS, I.NC.,805Albion Avenue • Schaumburg, IL 60193-4522

(312)351-.277.2

SALES FAX:(312)351-6930 SERVICE

See us .at U,e AGMA Gear Expo, Booth #124.

CIIRCLE A-18 ON READER REP~YCARD

-•

II

w.,.1 IIIIft I III..I- ,

-•

Rg. 4 - M!thinillg eltiImple of hard finishing No. L

TaMe 1Machining Examples of Hard Finishing

Frg.14IlS Fig. 16111 Fig. 18119 Fig. 20121122Eumplrl Ex;omple2 Example 3 Example 4

Number of teeth 41 32 Sl 31Module 2.54 1.15 .2 1.75Pressure angle 20' 15· IS" 17.5Hdl"mglr -11 -15.15" 29.S· -3O.SFiKewidth 21.5mm ]·/>.7mm I1mm 16.5mmApplication Is1Sprrd .3rdsprrdl lsi speed 51h spe«!

collarMOOinc Lion 01 It"rh 12"m !h tip ..,Hef In!rh !h/rhpr~u~ ..ngl~ slanting rh sl ..nling lip I\ft,e/ lip ,relief

by4"mProfile crowning In/,m 2jlm Ihl,h31'm Ih/rh.3l'm lh/rhljlmModiflcallon of Ihl0jlm Ihl5l'rn Ih81'm In 71'mhellx ilngle rhOl'm rh 12jlm rh lace mod. rhOjlm~;!dCTownirrg lhlm 2"m Iklrh 4 lim !hotI'm IhlrhSl'm

rh 2 I'mCulling material corundum CBN corundum CBNBonding + cerami nickel + ceramic nickel +blank whl!:t!l, '1""lwh~l whl!:t!J steel wheelPl'flnachinin~ precsh ..ved shaped hobbed hobbedslock rernoya!//l<ink 55"", 45 "'" so I'm SO"moOu..Jit)'''«'DtNl96.2 5 lob 5 6 6Surface roughness 2 I'm 1l'mw;th 3,.m 4/!mRm subsequent

line finish.Machining lime b1s«. 69 sec. 7ls«. 49SK.Too.! life I perdre-ssing cycle JOo!! total 8,000 of! 2S off total 1, JOO off

umber of dressingcyclrs 35011 - JO'off -

um~r M R'Ca.alingspertool - 5 - 5

Experience with successful modifications for noise reductionin wide load ranges demonstrate that what matters is corrnctl,ychosen modifications of the pressure angle and helix..a.ng1 withthe least possible crowning, As a rule, the drive flank and thecoast flank should be modified diffel'ently. Flank corrections inthe lead-in and lead-out area are carried out d gressively. In

Table 2Main Characterlsties of

Fine Fiinishinga:nd HOII'dFinishingFine finishing Hard finishing

Machineconcept

• development from modularystern 01greenshavlng

machine

• connected lo~d 12 kVA

• part is driven and brake lorceapplied to tool

'. stored-progt"m eorurol

• no additional motlens duringmachining

iii sa,me

• connected IcadlS kVA

• part and 1001 are kln~m~1 i .ally locked 10 a mol I r artransmission

'. C 'C controlled, two aArS

'. radial inJeed

I. sameTool '. ~"ternal gear, outsidediameter 2.lO mm

• corundum. synthetic resinbonded

• repeated dlftSing withdjamond dresser i pQSSibl~

• number of pieces pt', tool lifedep"nds on stock removed.number of work Erar teeth,hardening distortion. radialdeviation. quallty 01prema.chining, requIrementson quality !VOId. to beobtme<!

• example d 1.0011ifc:m - 2.2, Z - ,35

slock removal ,2 + 15 I'mdressing cyd~l 00 + 400 p.1Irhnumber 0.1 gears per 'ioolilleup to 8000 pes.

• corundum, ceramr~ bondi!'\ilor CBN coal:fd

• sam'!

I. s.me-stock removal 40 ... 150' I'mdressing cycles ] 5 + 6(1 patllnumber of ears ~r oeramltool. up' 10 1200 pes. number01 gt.us per CB 1001. up 1010,000 pc•.

Feed andInfeed

M05hingcondlrlons

• no longitudinal feednoinfeedconstant distance bet ....eeneenter lines

II continuous motion withouttrace 0.1 generated cut andfeed

'. crossed-axes angl.10·45'

'. single-flank machining byreversing sense of rotation

Ii'sameradial infeed

Part '. module 1.2 + 6 mm

'. oUfside diameter20+ 280mm

• Width of tooth l1;onkuploSOmm

• helix angl,e O· and ;I; 40·

'. 1 + 4 mm

'.4:5 + 250mm

'. uplol!imm

II same

Toothgeometry

• Rm srna ller than 211m po ible as required:'• .Rm - 2 10 S I'm (cwol!mcl• ,R", - 410B/LfTI (CBNl

• depending on quality ofprecutting

• on an average belt •• Ih.nquality srack 6 ace, DiN 3961

M.a.inir\g • "boul 0.5 min.tlme

• <kpendin./lan ~ininllcritena, aboul 1 min

November/December1989 3·3,

JEll: Robbersthat tnake sense

.' Why purchase a used gear hobber when youcan have a flew JElL automatic cycle

gear hobbing machine for less money.• 5 sizes available with hobbing capacity of

26"to 71"• Contact: HERMES MACHINE TOOL CO~•INC

5 Gardner Road· Fairfield, NJ 07006Tel.: (201) 227-9150 • Fax: (201) 227-9364

r------~------------------------~Cur our ami mail IOOUY[0:

HERMES· 'lACHINE lOOL Co. I C.5 Gardner Road •. Fairfield. .] 07006

'::) Please send me adduumal informanon on rhe JEI L. withcapacity: _

Namc ___

Company ___

~~~----------------Phone _

~------~------------------------~CIRCLE A·19 ON READ.ER REPLY CARD

Bring in new customerstor your business by advernsmq ,in

GEARTECHNOLO'GY,:1 The Journal of

Gear M'anufacturing ,.

I Mllbt.t1 ~HI ... _

Tillh"I~IInMa;unt t--:= ,I

ZJI'InR«N~ III Phi '"- '"

-I ==- --:......I~··~

}...- ,

- ,

-~ ..- .

II rIO1111 i

7. ..---1.1,

--l'-- I

, -Fig. 5 - Machlningexample of hard finishing No.1.

....

.'...VoI- 1

Fig. 6-Machinin8 example of hard finishing No.2.

I_H

TII! _to_-_ . .

• ad!-

Ill ...'

+ - ..... - ..

r-- ,llllilU'9'B"rrt "c .... !t.I!IIIlIiIiII,...

'~ --,pI!do_1'IIJ-..;, -.. tooIol, pIIcII_ rh

1ft- '

~T

..... DIIIrr~-""'~",,"=-=::--~~------""''''-----o_-_.......;.......;;.::-;.:;..;.!':.J,--? --

••

Fig. 7 - Machining example of hard finishing NQ. 2. Fig. 8- Machining example of hard finishing No.3.

The American Gear Manufactur,ers Association is ,oUeringseminarsconducted by recoqnized experts in the field ,of ,gear design andapplication. The latest techniques and information willi be examined.,g,iviingyou the most up-to-date technical information available.

December 5 - 6. 1989

Topics" Leeatlens and Speakers for 11989'- 1990 Series Include:

Loose Gear fnspection from the Customer's Standpoint; Los .Angeles, Calif.By Robert E. Smith; President. R.E. Smith & Co.

Gear Failure Analysis; Cincinnati, OhioBy !Eugene Shipley; Manager. Mechanicall Transmission. MTI. 'Inc.

Rational Gear Design and Lubrication; Cincinnati,. OhioBy Robert Errlchello; President, Geartech, Inc.

Controlling the Carburizing Process; Los Angeles,. Calif.By Roy E.. IKern; President. K'ern Engineering

Gear System Design for Noise Control; Alexandria, Va.By Raymond Drago; Chief Engineer. 80eing Helicopters

Registration incl'udes reference material, Iuncheon and coffee breaks. The costfor each one-day seminar is $295 for AGMA members 1$395 for non-members.A two-day seminar is $320 for members 1 $435 for non-members.

January 23,. 1990.

March 6. 19'90.

May 8, 1990

June S - 6" 1990

For Fur*her Iinformation Contact Bill Oanie'I!s:,AGMA Headquarter,s1500 King Street, Suite 201" Alexandria, VA 22314 • (703), 684-0'211

CIRCIJE A-20 ON READER REPLYCARONovember/DeoemtJer 1989 35

Preclislo:n ColletWOirk H'old'ing Device

for GearShav'ing

Easy Loading and Unl:oadingLoads Part On IyReduces Operator FatiguePositive Positlonlnq

D:REWCO CORPO,RA.TIONPrecision, Workholdlng and' Tool Holding Devices

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CIRCLE A-21 ON READER IREPlY CARD

order to be able to use the least amount of crowning, the admissi-ble pitch errors must be kept small. This will permit at the sametime, the best possible distributions of contact and root filletstresses in mesh for critically high load stages with the least possi-ble influence of additional dynamic forces. In other words, apartfrom improvements on the noise sector, considerable increasesof the load capacity will be obtained.

Gear Noise with Hard. Finished and Fine Finished GearsFig. 13 schematically shows the possibilities offered by the

hard machining processes in order to counter the noisegenerated.

A reduction of the gear noise will start with the implementa-tion of tooth gearing data (face width, helix and pressure angle,addendum modification factor ,and high too th design, etc.). (3,6)

The aim is to obtain a maximum contact ratio for smoothing themodulation of rigidity and to choose a contact ratio of an integralnumber of teeth, taking into account the contact conditions

36 Gear Technology

M,&:bl,u

1l1li,.144Ao.IflrJs.ri.INr

K.iIIIdIIINuc~Nf.:

+

+

.. I

+

+

I~n~ ~Lm~. ,.c;i'olli FWi'I(, I

~""".O ... t:tIJLWIrl.Ou.l_I~iIIi)waJ.IULfMlUlOiuoI

.......,. :ouatiill.WIiirI 0iJaI.RuMt&ull.tIWtII/;ilwng , ~~ __ L-

fig. 9 - Machining example of hard finishing No, 3,

..........fJl!.linAlrblllAl_i.l~~a Mi • _

'MI r.~"":1!1~P10f --.ct. .~__•

r.:;I'IlijlfWlUi...,II

•

ZR\ -]J)J.•~ ...... ti

II.U,' -II

I,"",,,!~ Fllnk8n~lnII!/Erzerugl!lfJdfl' 0- II

~....'""V._ I

.. ~ bi'oti I :IiM'HI .fI6I1 uaJ~ wI. I I • _~_ III I ~t'l

fig. lO-Machining example of hobbing No, 4,

I IM.IbI.t:t "' , ..

_ """ FIonkonlW. ...... __ Pwooc.w_ ..• .......... ~

10. . , - PJgt MJIMr L.. ~.i.litlrJIildlIIIiI=- , ~n_.:_~~~~KlNlJIMMaIt ..... '.~ ~21 - t..... ~111 -« 1I'ruI~'IiI;"'4' "

.... 1'WiiIiIo Pool!! 1'Kt!W~

-! ~III '"p". ~ f[CmITU}...-,..-.I---,I it =1

•a..-•... . ! , . .... , I"

.~ m <\II

,,I. •II ~~;I • o. j '. 'II

I -- lO Flan""""nJoJ Ermtgti>IIo 0 ..an.,1IinU- III IMd III

~. ;!II TTT TI ""' \"...-

~'_I i

'I--- I I~I•.i ,~ , 1J.,I'

~~~.~! 1;.lL.!. ""'-I, ,":, --- • ,. I I • " 1 ",.;l.....- u . ., ~:lt, ,

Fig. 11- Machining example of hard finishing No.4.

I TeIIunprMIllln;g:-. ..~ .

T..II!ung~f'""NriIl.f1&ni1

_1~_1h --'. I

+

- , Itr,

~,o...i .rwl.1!IWW1~QaI. ~,c..I 1M'"

tH

+II!!! ,!!!II

.. ,~ JijI .... OioIIII

UI.. '. 1,

Fig. 1J - Machining example of hard finishing No.4.

JAMES ENGINE'ERIING_

11707 McBean DriveE,I Monte, California 91732

(818) 442-2898 Booth #234

* Compact Design: Ideal for cell envronrnerus.

* Durable: De~lgned to meet production demands.

* Fast set up and operation: Most set ups made In less than I minute wnhryplCal cycte limes of I minute Of less

* Portable: WJlh optional can it can be moved from WOf~ station towork station.

* Fast chucking: OUickly chucks most par~ WI[hOut costly and timeconsuming speCial tOOling.

* Vernier Scares: Vernier scaleson the adjustmem axes allow quick andconsistent repeat setups.

* Modular Design: Opncns Install and remove In seconds.* Versatile ~~~; With tile optional equipment practIcally any Iype or

gear and edge finish can readily be achieved

CIRCLE A-22 ON READER REPLYCARD

under load. The modification band width should permit a con-figuration of the tooth pattern that wiD allow no erratic varia-tions of rigidity ..Only a defined tooth bearing development winpermit a modification of flanks for a wide-band load range,Otherwise heavy noise win be generated mainly in the partialload range, since the rather unyielding partial-load tooth patternwill result in a contact ratio ofa non-integral number.

At the same time, the tooth contact pattern should have suchan ease-off geometry that neutralizes deviations caused bymanufacturing and faulty meshing due to the load is minimal,

A conclusion drawn from these circumstances is that onlyatooth flank design specifically adapted to the possibil.ity ofadefined tooth pattern will be able to make full use of the essen-tial advantages of hard finishing .

The practical procedure for defining the modificadons can beascertained by checking the tooth pattern, as with copper-platedgear flanks, with the gear unit in actual operation.

November Ioeeemeer 198937'

Flank Tooth 'Composit.modificatio:n contaGt awl.tion

De'forml!lUons ofhousing,shafhi.bearings underLQild, thermalinnuences

Tooth distortionunder load,,meshing impact,pitch error

Dls.tributjon ofpressure underload, ~tter DfproductionIoleranC(ts

T<>P<>Iegi""lIyoptimiztJd n'ankgoo-melt)'

Fig. 13~ Systematic diagram of superimposed modifications of flanks for noisereduction. .

--.om'V

5 mV/Div.

IE. 45 mV

mV/'Di¥.

+: I - - - - r - -lies (tonesloo ...

I

Fig. 14 ~ Frequency analysis of the airborne noise of green shaved gears.

&,_ noI .. /CIoc'_·-",fundamental' !requency:I ... 800 Ii> _ finiol>e<l, '01 rnodj!lcation

4D mV

5 mVlOr..

:8-35 mV

mVIDiv.- - --'-

I1 ...... -T--T-- hormon .... (pure _.

+ 1 I I I +1 I1 I

1 --I 'IlIIrrow-banded genention

1--1 I-.~ ~

;JV IJW~ J\.~,

_, 1.6 KIt. 4.8 KHz 10!t~800 1Hz 2.4 KHz

Fig. 15 - Frequency analysis of the airborne noise. of hard-finished gears (firstdesign of modifications).

38 Gecr Technolog,y

+

The first step is to define the modifications of the helix andpressure angles.

These modifications differ for the drive and coast Hankgeometry according to the deformation behavior of the systemof shafts and bearings, as well as of the gear housing.

Angle modifications are defined for a characteristic load stageof the gear set by evaluating the tooth patterns. According tearecognizable trend, a flexible grinding process is used to providegears with modifications that will cover the estimated area ofmodification. These tests will be continued until satisfactory con-tact pattern (no noise behavior) is achieved.

The second step is to define modifications which will lay downthe band width of the admissible load range and which willneutralize a scatter of deviations caused by manufacturing on ac-count of production tolerances. Mainly,this would concern pro-file corrections in the lead-in and lead-out areas or addendumand dedendum areas and superimposed crownings.

The procedure is the same as explained above, though in thiscase the preset load range will be investigated step by step.

Effective modifications for noise reduction are characterizedby an unerring choice of angle modifications and by the leastpossible superpositions of profile corrections and crownings inthe range of a few p.m.

The effectiveness of these modifications will essentially dependon the very dose scatter of production tolerances of the gears.For instance, pitch, profile, and helix angle deviations couldreduce and even neutralize the effect of such modifications ...

In the following, a noise reduction on a test rig will be de-scribed by way of example. A frequency analysis of the airbornenoise signals was carried out.

A green shaved pairing of gears is used as reference (Fig.,14).With the frequency analysis, the partially stochastic distribu-

tion of amplitudes in Fig. 14 is striking. Though the first har-monic dominates, it is not noticed subjectively as such in thenoise.

In the following, the gears were hard-finished with two dif-ferent modifications.

The first design of modifications supplied the distribution ofamplitudes shown in Fig. 15. The modifications were establishedfrom these green shaved gears running particularly smoothly.The amplitudewith fundamental frequency (800 Hz) diminishedmarkedly.

With the harmonics, however, a momentous narrow-bandedrise of amplitudes occurred,

This narrow-banded generation, especially of the first har-monic, is subjectively disagreeable. The narrow-banded genera-tion came into being due to an accurate gear, geometry(especially the very small pitch error) with unsuitablemodifications.

So far, the transfer of modifications from green shaved gearshas not been successful in all cases, since the necessary crown-ings required by hard finishing are much smaller than for greenshaving, because for hard finishing correctly selected modifica-tions of the helix and pressure angles with minimal crowningsare of prime importance for getting best possible contact ratio.The second design of modifications will have the distribution ofamplitudes shown in Fig. 16.

The marked drops of amplitude with only slight relative pro-truding amplitudes, and the consequential wide-band quality

--_ ~ ftootoOIU Itwd---.2nd ~. ~~- ~~40 mV

5 mY/DIY.E·~mY

flN/Dfo.-----I T t--

+ : ~-.j--r-T-r-(--I +I I I I

I I ~ I I

I I I I II I I I I

I

I I

~ AI

I !

~'J UWL fvJ\-.!.!!!.i .1 Itu1!11Ot1. IIOtI

UIQIr 10KIUtoO 2A

Fig. 16 - Frequency analysis or the airborne noise of hard-firushedgears (seconddesign of modifications).

-- _--,2nd __ ."-"r. I.-IOOIU

40 mY

5 mY/DIY.I--I--t-+----+----------\ ..E-U mV

~+_4-~~--~~-~7~-----__------~-·-~-~*"-·-(-~-·----~i+f-i---.----f----+----------l: --ge,-- .....I---Ir-...-J-I-~-;.--II;-\, - -""~ ... ~--- -

Fig. 17-Frequency analysis of theairborne noise of hard-finished and finefinished gears,

provide a good subjective noise impression, since no individualtone made ilself markedly heard.

In. the next step of improvement the microstructure of flanks,with a roughness value Rzo ""'.3,.un was reduced to Rzo "" 1ILIIl by fine finishing without changing the geometry, Fig. 17shows the resulting frequency analysis.

The peaks of amplitudes with reference to Fig. 16 were furtherlevelled. The subjective noise impression was especially improv-ed for the well audible frequencies, If the noise relative to Fig. 16still produced a sound impression, the noise relative to Fig. 17increasingly merged into a noise similar to wide-banded rustle.The noise improvement, however, should not be primarily at-tributed to a reduction .of surface roughness, but to the removalof microgeomefrical meshing faults.

VVhen investigating the deflections of gears on the test rig,marked acoustical differences were obtained in specific deflec-tion and speed stages. requiring .additionalselective modilica-tions of the flanks or da.mping methods for the natural frequen-des of the gear blanks.

The strategy of defin:ir\g modifications also consists in pro-

viding the results obtained under ideal testing conditions in sucha way with a modification band width so that good results areobtained even in actual operation of the gear unit under vari.ousload stages. The modifications ultimately found and specifictooth gear quality parameters must be Evequently kept at closertolerances than required in the average quality specifications inorder to obtain optimum noise results. Likewise, high demandsmust be made on the quality of the gear housing and to thesystems of shafts and bearings if the noise reduction is to take amaximum effect..

SummaryStarting from the geometri.cal. and qualitative :requirements

made on hard finishing methods of gears using geometricallyundefined cutting edges, a brief survey was given on suitable toolconfigurations, the kinematical c-onditions. and possible drivemodes for hard finishing and for nne finishing. (See Part U

The importance of tool manufacturing and the pari: played bycomputer assistance fer tool design were dealt with. Machinjngresults demonstrated the efficiency of the hard finJsrung methodsof gears. Finally, the basic procedure to be followed forestablishing tooth flank modifications for noise reduction werediscussed.

References:1. GOEBBELET, J. "Tooth Contact Test of Cylindrical Gears,"

Dissertation, Tl-l-Aachen, 1980. (In German.)

2. KLOECKER, M. "Noise Reductions of Machine Tools." Disser-tation, TH-Aachen, 1982. (In German.)

3. LACHENMAIER, S. "Design of Special Cylindrical Gear Teeth.for Vibration and Noise-Reduced Running." Dissertation. TH-Aachen. 1983. (In German.)

4. BAUSCH, T. el al. Gear Production Methods. Expert-Verlag,Sindelfingen, 1986. (In German.)

5. NEUPERT, B. "Computation of the Tooth Forces, Contact andRoot Stresses of Cylindrical, Bevel and Hypoid Gears .." Disser-tation, TH-Aachen, 1983. (In German.)

6. WECK, M. - "lmprovement in the Field of G ar Technics."lndustrie-Anzeiger, 109 (1987) 90. (In German.)

7. SCHLEICH, H. "Sharpening of CBN Grinding Wheels." Disser-tation, TH-Aachen, 1982. (In German.)

8. SCHRIEFER, H. "Computation of tn Rank Geometry, Con'tact,and Running Conditions of Bevel and Hypoid Gears," Disserta-tion. TH-Aachen, 1983. (In German.)

9. STADTFElD, H. "Practical Compulerized Design of BeveJ andHypoid Gears." Dissertation. TH-Aachen, 1987, Un Grman.)

10. STEFFENS, K. "Thermo mechanics of Grindi.ng." Dissertation,Tl-l-Aachen, 1983. (In German).

11. WECK, M. Machine Tools, Automatic and Control Systems.VOl-Verla.g, Dusseldorf, 1982. (In German.)

12. \AlERNER, G. "Kinema.tics and Mechanics of Grinding Processes."Dissertation. TH-Aa.chen, 1971. (In German.)

13. KONIG, W., STEFFENS, K., WERNER, A. "ComputerSimuJa-tions of Grinding Processes." lndustrie-Anzeiger, 109 (1987) 68.(In Cerrnan).

Acknowledgement: Reprinted courtesy of Society of Manufactun'ngEngineers. Presented at the 1987 Gear Processing and MClPlufacturingClinic, Nov. 17-19, 1987, Southfield, Mi,

November/iDecember 1989 39

COMPUTER~AIDED ...(continued from page 11)against the allowable values. If the checkis successful, then the preliminary stage ofthe design is declared complete. It is sug-gested(2) that the face width not exceed 5pand be at least 3p where p is the circularpitch. Dudley(l) suggests that the facewidth should not exceed the value of thepinion diameter. So, if the calculated facewidth meets both of the above criteria,then the preliminary design is complete;otherwise, the initial pinion tooth numberselection is revised, and the process isrepeated until a satisfactory value of facewidth is found, Notice that if theminimum tooth number criterion is notmet, a new class of materials based on arevised Bhn value is selected, and thedesign process is reinitiated.

Design. for Strength and DurabilityAfter the preliminary design, the tooth

must be checked for strength and durabil-ity. Calculations for tooth strength andsurface durability are based on the unitload and the K~factor. (1) Unit load is afactor which is a measure of strength of thetooth while the K-factor is a measure ofsurface durability or resistance to pitting.

The unit load is calculated based on thegiven information about the horsepower(HP):

V. - HP * P * 126050,-n*d*F

where d = pinion pitch diameter (inches) ..The calculated unit load is now incor-

porated in the formula for tooth strengthevaluation. The formula groups all thegeometric design variables into essentiallythree factors: (1)

whereK, = a dimensionless geometry factor,Vr = an index of load intensity (unitload),Kd = overall derating factor for bendingstrength (psi).

The geometry factor is a measure ofshape of the tooth and its effect on the ben-ding stress. Factors such as the depth of thetooth, pressure angle, and adden-dum Idedendum ratio are incorporated inassigning the geometry factor. Index. of

Ca.ni you do effective case depth studiesin2 mlnutes?

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CIRCLE A-24 ON READER REPLYCARD40 Gear Jeohnolog,y

load intensity is designated by the unitload. The derating factor is an index to ac-count for the non-uniform load distribu-tion across the face width. It also takes in-to account dynamic overloads due tospacing error and the effect of the massesof the pinion and the gear. It also compen-sates for other quality related concepts,such as surface finisheff:ect overloads dueto non-steady power, and metallurgicalvariations between small and large sizegears.

Overall derating fador is defined by thefollowing formula:(l)

K - KmKaK•d-

KvwhereK, = application factorKm = load distribution factorK, = size factorK, = dynamic load factor

A similar derating factor can be defin-ed for the tooth surface durability:(l)

C - CaCmCsd-

CvwhereC, = application factorCm = load distribution factorC, = size factorC; = dynamic factor

It is assumed that all the factors con-stituting durability and strength factorsare the same except the size factor (C.) ..From the standpoint of surface durability,face width is probably the best way toevaluate the effect of size. (1) The size fac-tor for durability is generally intended forderating of gears based on metallurgicaldiscrepancies between large and smallergears.

The rules of thumb employed for thesize factors are(l)1) For face widths up to 5", the size factor

is set to 1.2) For face widths greater than 5" and up

to 16", C, is set to 1.3.

The level of reliability chosen in thisparticular approach is L1 (expected lifewith 99% reliability). However, one candefine several reliability factors, depend-ing upon the nature of the design needs.Based on the level of reliability and thenumber of required life cycles, the allow-able values of strength and durability canthen be obtained from the material

CIRCLE A-23 ON READER REPLYCARD

Table .3

......'217:!iOO

'45000

1 1'16000

z I 87000 ii... 72 !iOO ~Ii 58000 iII

;;

I

f 43500 ~I J :

29000

217~'

Fig. 1- Bending strength versus life cycles'".

database (Fig. 1). The calculated bendingstrength and surface durability are check-ed against the allowable values, If thecheck is successful, the design is accepted;otherwise. the selected number of teeth isdecreased until a stl'onger gear design isachieved. or the minimum allowablenumber of teeth is exhausted. If the latteroccurs. ehen a stronger material is selected,and the design process gets underway.However, if the material data base is

ApplicationParameter Reference 131 Driven

P,itch,(P) 4 4

10iameter (d)4.5 4.5,'Inches]

Face width (F)3.41 3.38[Inches]i

depleted, then failure of the design isreported. At this point the user is advisedto consider an alternative gear drivesystem, such as helical or epicyclic ar-rangements ..The flow of information inthe spur gear design methodology isshown in rig 2.

Example and Discussion.The example is a.comparison between

the textbook approach described inReference 2 and the application-drivenprogram proposed in this article, The ex-ample essentially states the foJ]owing:

"A pair of 41:1 reduction spur gears isdesired for a lOO-hp 1120-rpmmotor . The gearsare to be 20. full-depth with a clearance of O.250/Pand made of UNS G-I0400 steel,heat-treated and drawn to 1000° r.Make an estimate of the requiredgear size."In the above example, the authors(2)

Fig. :2 - Flow chart of the spur gear tooth designprogram,

use a factor of safety of four and thematerial is predetennined. Incontrast, theapplication-driven approach requires theuser to identify the application environ-ment only, For this particular example. ageneral class of hi.gh-speed drives isspecified as the application environmentfo·r the spur gear design. Results for bothapproaches are shown in Table 3.

As can be seen from the table, bothmethods yield similar results. However,there are marked differences in the ap-proach. Shigley and MitcheU(2J assume aminimum pinion tooth number of 18anda pre-established type of material. In theapplication-driven approach, theminimum tooth number is initiaUysetto15, and the program establishes 18 as a.viable tooth number for the pinion. Also,the material is selected from a data base ofavailable through-hardened steel. Notethat this data base can be updated ifnecessary, and new types of materia] can

(continued on p.age 47)

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DIS,fRICT SALES IMANAGER(East Coast}

KJin~elnberg, ~ worldlleade.r in gear·makmg machinery and diagnosticequipment is seeking an expert-enced ca,pUal eq,uipment sales en-gineer to manag~ sales for IEasternPA, INYC, NJ,. D,E, a_ndMD'. Froman lEast Coast base, the person wiBalso work with rep orQanizations inINew England. Knowledge of ~heGear-Machine Tool lindust,ry is 'es-sential. Klingelnberg offers the rlightcandidate a cornprahenslve com-pensation & bene1it packa.ge. SendiIletter and resume to: IEmst LoNel-mann, VP-GM, Kling:elnberg Oor-poration, 115200 Foltz lndustrialPkwy., Cleveland, OHl44136.

<0> KLIN~EL.IE'RG,...Ruts it all tOt1ethaf.

ENGINEERSFunk. Manufacturing. a subsidiary of Deere ,IlkCompany. has been long known for itstradition of Leadership. Quality and Ennovatlon in the manufacture ,ofoff-ro- d powertransmission equipment. Seeking to, compUment our existing manufacturing servi.cesorganization in Coffeyville, Kansas. we are 'CUf11entlyoffering exciting opportunities fol":

Mana2:er., Quality AssuranceThis position will be accolilDtab'lefor the quality of the company's proouctsand th.eiNlosteffectiveness. CandJdates should posses ..a degree in engineering or technology fieldswith 10-15 y,ears experienoe inquality as_ urance assl.gnments. A. strong backgroundmmetalworking industries is required and power transmission product ,experience is

I prderred. Must possess a working knowledge 'ofTOtal Qualiity Assurance methods suebas: statistical process control (SPCI.design of ,ex.peri.ments , andadvanced quality plan-ning systems.

I _ •... . .Ma:nufact~g Ene:inee~ ..Reporting 1:0 the MlUlufactunng services Manager, di'is. position win be r1!Sponslble formanaging complex capital projects in anadvanc,ed macb.ii:lI~shOp,envil'onment., Qualifiedcandidates should possess BS degree inengineering or technology disciplines and have5elO years experience inmetall ,Clltting Industries with emphasiS on CNCma.chlne toolsand project engineering ass~,gnments. Gearma.nW'actu.rlng experience would be·h.elpful.

Product Design, En,e:ineerThis position will berresponsible forthedeslgn and apPllcation of power train equipment.Qualified 'candidates must have a technl.cal degree and. a minimum of three years ex-perience in .applicable power train component. environment. QualUlcaUonhouldi in-,cludeexposure to,CAD/CAM. gear design. product testing and applications ,engineering,

These posi.tions offer a salary ,commensw:ate with your level of experience a. well as aliberal [ringe benefits paCkage and reiocarrcn pr,ovisions. QualU'ieClicandidat,esshould I

forward their nsume with salary bistory in oonfidence to:

s,n WaageDirector. Human .Resources

FUnJc Manufacturing ,CompanyP.O. BOK577

Coffeyville, KS 67337Equal Opportu_nity Emp'loyer M/F

Bell Heli opter Textron Inc. 1r cognized as 'In world's leaderin 'the design and manufacture ofadvanced 'technology rotor and'liltrotoraircraft. We are seekingspecialist to h Ip meet thechallenge posed by the next g n-eration of rotorcraft, the multi-

srvic V-22 0 pr y TiltRotor"andthe U.S. Army LHX.

TRANSMJSSIONDESIGN ENGINEERS

Heli opters require light-weight, sophjsticat d hans-missions to transmit powerto the main and tail rotorsystem, and Bell is in theforefront of d ign and manu-'facture of uch transmissions.

These posi nons require a B5Or M5 level engine ringdegree and 3 to 10+ years oftransmission de ign peri-enc . This experi noehouldinclud overall gearbo·de ign and evaluation. in-cluding gears, coupling,bear.ings and shafting. A ro-space indu tty expert n ewould be an asset, but is,notrequir d.

Technical. is ue indudweight avi:n,gsand control,s~ructlU'aI int grity, vibrationand noise reduction,

Knowldg of CADAM andexposure to CATIA 'Would bea plus,

Bell off rs competitive sal-ari s and a top benefitspackage. Please s nd yourresume in eonfiden to:

Employment Replie-enta'HveBelli Helicopter Textron Inc.ao, Box 9OlID4Dept TS-QQFort Worth, TX 761011

l1-tE 'FUTUFIE IS QUFlS BY DESIGN""

1III1Ik1ll1lll1l" II :t:, II Lt.: : Ii'~t."IfXIr1_

C' ltei BEu'- HEl.!COf!TER TEXTRON INC.,if,N EQuAL OI'I'OA1\!NITV EIoIPI..I1tER,!!I1I'IIW

November/December 1989' 45

EMPLOYMENT OPPORTUNnlESIintemational Gear Corp., a.manufacturer ,of precision transmission ,parts fm the aerospaceindustry with sales of $25 million, has immediate, EMPl:OYMENT 'OPPORTLINITIES lintheir Cleveland, Ohio facility. The following openings currently exist

GEA'Ft ENGIINEEFtB.S. inMechanical Engineering. The successful candidate must have five to seven years',experience in all.aspects.oI gear gr;inding, gear cuttingl and gear generatingl for st,raightcut, helical, spur and' spiral'-bevel gears. Familiarity with Quenching and speeial processapplications for gearsa. plus.

'0'.0./11.10. GRINDING SU'PER;VISOR:Suc¢essfuJ candidate must have thorough "hands-on" knowledge in O.D.lLD. Grinding.Thr'ee to five years' supervisory experience in a.manufacturing environment working withclose tolerances on precision machine parts. Ability to read and interpret complexblueprints ,and operational sketches Irnaccord'ancewith .ANSI Y14.5 metric geometricdlmensioning required. Must a/so' possess good people skills.

IPI~ANT METALILUFilGISTSuccessIul candidate must possess a B.S. in Metallurgy with five to seven years' ex-perience ill Heat Treat and Plat,ing of exotic metals. Must have knoWledge ot quenchingpress and vacuum carbonizing! processes. :FamiHarity with 'gear technology a plus.

T'COL IDES:IGNERAssociate's degree linTool Design or equivalent. Must be familiar with ~NSI Y14.5. Threeto five years~tooling experience. Familiarity with quenching tOOling a plus.

'QU.AILIITV EN:GIINEERB.S. linMechanicallEngineering' perferred. Knowl'edge of MIL-O-9858A,MIL.STD-1520Cand .ANSI Y14.S. Strong background in gears. Understanding of manufacturling andspecial processes for gears .. Dedication to a proactive quality system. Knowledge ofgear inspection.

QUALITY IENGINEERCollege degree (MetaUurgy preferred) ~equired. Knowledge of IMll-O·985BA, Mll-STD·1520G and ANSI Y14.5. Strong background in heat treat, plating',. metallurgy andNDT~Understandingl of special pfoc,esses !'squired in aerospace transmission man urac-turing. Dedication toa proactive, quality system.

We offer a competiUve salary, comprehensive benefits and the opportunity for growth andadvancement To take advantage of these opportun ities, qualified candidates -should for-ward their resumes in oomp'lete contidernce to: Manager, RecrUiting, INTiER~ATiIONAlGEAR OORPORATiION. 23555 ElICLlD AVENlIE, CLEVELAND, OH 441117.An EqualOpponunity Employer.

INTERNIATIONALIGEARIGORP.

Service EngineerExp. repairing, hobbingl& shaving,machines. Company will pay to re-locate to Richmond, VA Salary30K.Call Quantum Careers, Sue Spease'11..fK»446..98S2.

IGEA!R MANUFACTU.RINGIDlr.clo:r'DIMlnll1aolurlng:$70.000 - Aircraft/Industrial1[lnlrtl MlI1lgtr: $52,000. Custom Gear ShopIMlnullclllrlngl Englneers/ManagoR:

$45,000. Automotive/AircraftiDnlgn/DIYIIDpm4lll1 Engineer: $45·.000PI'IICIII Englnllrl: 54.5,000

Ann; Hunsucker. Excel Associates. P.O' Box 520.Cordova, TN 38Dll1. 901-757'9600, fAX90H54·2896

GEAR P,ERSONNEILIENGINEERS

GEAR GRINDERSIMACHlNISTS

IMlANAGEMENT/SUPERV,ISrONPRODUCTION OONTRO.L

QUALIITY ,CONTROUINSPECTIONPURCH'ASING MAHAGBii

SALESACR has moved tOB new 85,000 square footfacility in Mt. Clemens, Michigan. As a l'8Sult~the above· and other ,new positions. are beingereated, If you aJleIn the the· gea!' buslness inany ,ca.pacity, Brie ambitious ,and thinking 01'makIng a mOve, send us yoUI' resume, -

ACR INDUSTRIES, INC.15375Twe.nty-Thr Mile Rd

',

,MI•.C .emens, II 4BQ44...96S0

MtiiNUFACTURINGPROCeSs, IENGINEER!

.A. high quality custom gear manufacturerwith rapid growth is expanding its engineering

! staff In the area of estimating, tooling and pro-

I

cess routing.If you are int9l'8stedl in improving your salary I

and growing witih us while helping to improve·our engineerlngl and manufacturing pro-cesses, we would like t.olalk to you.

II you have al leasl five years experiarncEl inIhe gear industry, doing estimati ng or processengineering, sand your resume and salaryhistory to:

J. Graves, Vice' President-MIg.Patterson 'G.ear ,I Maclllne ,.-IIIC.5876 Sandy Hollow RoadRockford., Illinois 611109'Phone (815) 874-4327

I IPOSIi110NWANTED: Broadly ,experiencedI Gen:emllMal1agerwith a.proven record 0128

years in aero·space, military and commercialmar,k.els.IP& L.~esllOnsibility at a division sup-plying precision gear products to Itleaeros,pa08market.Sucoessfully ,improved productivity Ilevels,established a close customer relations'hip andstrengthened professional staff performance.PI'easesend reply 10:IBoxfT, 'Gearlechnology,P.O. Box 1426,.Elk Grove, IlL.60009'.

G'~aring_UpTo Afe',e'" New Challenges

AHROWG:EAR COMPANY,llocaledl iMuburban ,Downers Grove, nnnols, is a leading manufacturer 01 high q,uality gears. With ourmost recent pian.! addilion we now t\a,veap,proxlmal~y 2OO,OOOsq,uare,feel In three plants. In the last 5 years over 10 million dollarshas been invested in the lalest eNe Machine' Tool Technology general.ingthe following openings;

SENII,Q'R IPROC'ESS EN,GI:NEIE,RCandldats, should have' ,8 background in planning operational sequences and heat !reallng (Carburize, Harden and, Niillide) 01'so-pnisticateel transmission component parts. Prior experience in a gear manufacturing 'envlronmnenl is a,must College and CAD/CAM background would be plusss,

TOOll IDIESIGN ENI'GIIN;e,EIRPrevious,experience In agear manufacturing environment Is required and CAD/CAMba.ck.grounclwould be a pius,. Candidate mustIbefamiliar with the tooling requlred for the -machining and heal treaUng (Carburize, Harden and NlIrlde)of alrcr,aUtransmissioncomponent parts,

AIRCRAFT' GEA'RB'OX ,ASSEM'B,L'ERCandidate must be'ablato.read and Interpret military and aircraft specifications as well as inlrlcate bl ueprints. Previous experience:sl1.ollldinclude' working k:now1edge of assemblygallg.ing eqllipmenl and tools.IExceiIent salaries, ,comprehensive benefits and relocation assistance provided.We' invite you 10, investigate, these' outstanding opportunities by s&nding,a resume including salary hlslory In con'fidence 10:

COMPUTER AIDED ...(con.tinued from page 42)

be added for any particular appli.cati.on.Hence. selection .of pr,oper material is anintegral part ofthe gear tooth design pro-gr~m ..Also •.the gear tooth data. obtainedvia the app1ication-driven approach in-earperates the strength and durability fac-tors, These factors inherently carryameasure of safety to the gear tooth designprocess. and, therefore, introduction ofauser~efined factor of safety becomesunnecessary.

This approaeh incorporates the expes-tiseof the gear designers into the designroutine. Theeepertise is obtained fromhandbook inlormation. and can beI1egularly updated if necessary. Conse-quently, no preccnceived iruo.rmationabout the type 'of material or the factor ofsafety is required to arrive at an aoceptabledesign decision.

ConclusionA new '~echnique for computer~aided

sizing of spur gears has been proposed!.The method has suocessfully been im-

Human Resources,Ar:r,o,wGear Company2301 Curtiss StreetDowners Grove, III 605115

An Eq,,~ Opporlumly Employ., M/F

plemented in a comprehensive parallelaxis transmission design expert system. (5)

The gear tooth design is application-driveand is based on the index of tooth loading(K-factor). Results show th~t the techni-que could lend itself to modular expansionto include other types of gear teeth designsor different application 'environments.Once the K-factor has been established forany new application environment, i't canbe stored as the basis for the gear toothdesign for that particular application. Thisin tum, suggests applying a rule-based ex-pert system architecture to continually up-date the knowledge base of applicati.on orK-factor values. An Lntelligen:t materialdata base search routine can also improvethe options available for gear materialselection.

This article presents a first step towardgear tooth design automa'tion incerpor-a'ting the expertise and experience 01 thosewhose endeavors led to the now estab-lished AGMA standards for the gear de-sign. A logical next step, in this processwould be the inclusion of helicalgeardesign and theexpertise in determiningwhether at set of spur or helical gears are to

be employed for a particular design en-vironment. The goal. is 'to'merge 'the geardesign techniques with the state o.f the artin eomputer-aided design methods. whichincludethe expert knowledge at well asroutin.e compueational methods.

Ref£renoes:l.DUD1E:Y, D.W., Handbook of Practical

Gear Design. McGraw-Hill Book Co.,1984.

2.DUDLEY, D.W., 'Gear HandbOOK,McGraw-Hill Book Co., 1962.

3.SHIGLEY. J.E.,and MITCHELL LD.,Mechanical Engineering Design. McGra.w·Hill Book Co., 1983.

4.I.YNWANDER, P., Gear Drive Syst,ems:Design and Application. MarneIDekkt!l.1'983.

S.ZAREFAR. H.,. LAWLEY, T.,. andITESAMl. P.. '1lAGES: a Parallel AxisGe.ar-drive Expert System," Pfocftdings1986 ASME Internalional Compute:rs inEngineering con£erenc, Chicago, pp.14:5-147.

AcImoWlftlganmt: Reprinted' cauTtl!5y of A mmeanSociety of MKhaniaU En~, from thB frooeedinp01 ,the 1989 llI~ematiol'lAlPower Transmissi nandGe ring Confe~. Vo.l. I. pp. lC17·UO.

INovember/December 1989 47

Booth No. 134-36-38AGMA1500 King Street, #201Alexandria, VA 22314(703) 684-0211

Booth No. 319"INDUSTRilAL HECTRlC HEATlNGP.O. Box 991Warren, OH 44482(216) 372-8506

Booth No. 114-116'OERLIKON-OUHRLE LTD.Birchstrasse 1558050 - Zurich. SwitzerlandPhone 01 /31622 11

ADVERTISERS' INDEXThe advertiserslisted below will have booths at Gear Expo '89 .

•As Seen In Pre-Show Issue.• ,As Seen In Show Issue.

Booth No. 301AMERilCAN PFAUTER CORP.925 Estes AvenueElk Grove Village. IL 60007(312) 640-7500

Booth No. 339•• J.R.M. rNTERNATIONAl5033 East State StreetRockford, It61108(BI5) 397-8515

Booth No. 124PEELCO MA'CHINE TooLS,INC.815 Albion AvenueSchaumburg, Illinois 60193-4522(312) 351-2772

Booth No. 125CIMAU.S.A.SOl S. Lake Blvd.Richmond. VA 23235(804) 794-9777

Booth No. 234lAMES ENGINEERING11707 McBean Dr.EI Monte, CA 91732(818) 442-2898

Booth No. 301PFAUTER-MAAG CUTTING TOOLSP.O. Box 29501351 Windsor Roadloves Park, It 61132(815) 877-0264

Booth No. 343Lees-Bradner byFAYSCOTI225 Spring StreetDexter, ME 04930(207) 924-7331

Booth No. 101KLINGELNBERG AMERICA CORP.P.O. Box 3602615200 Foltz Industrial Pkwy.Strongsville, OH 44136(2161572-2100

Booth No. 102• 'PROCEDYNE CORP.221 Somerset StreetNew Brunswick. NJ 08901(201) 249-8347

Booth No. 507*FUKUYAMA & ASSOC.3340 San Marcos Dr.Brookfield, WI 53005(4I4) 781-4245

Booth No. 239-338"KOEPFER AMERICA, INC.555 Tollgate Road, Suite CElgin, IL 60123(3I2) 931-4121

Booth No. 243REISHA.UER CORPORATION1525 Holmes I\oadElgin. Il60121-7458(312) 888-3828

Booth No. 335• "GMf MUTSCHLERr.o. Box 193Clarendon Hills, .It 60514(312) 986-0756

Booth No. 213M & M PRECISION SYSTEMS300 Progress RoadWest Carrollton. OH 45449(513) 859-8273

Booth No. 119SHORE METAL TREATING, rNC.5475 Avion Park DriveCleveland, OH 44143(2I6) 473-2020

Booth No. 420GEAR TECHNOLOGYP.O. Box 14261425 Lunt AvenueElk Grove Village, IL 60007(312)437-6604

Booth No. 311MITSUBISHJ HEAVYINDUSTRIES LTD.873 Supreme DriveBensenville, IL 60106(3I2) 860-4220

Booth No. 201STARCUT SALES, INC.P.O. Box37623461 Industrial Park Dr.Farmington Hills, MI 48332-0376(313) 474-8200

Booth No. 236"GUEHRING AUTOMATION, INC.P.O. Box 125W227N6193 Sussex RoadSussex, WI 53089(414) 246-4994

Booth No. 237"MULTI-ARC SClfNTJF1CCOATlNGS200 Roundhill DriveRockaway. NJ 07866(201) 625-3400

Booth No. 220NEW AGE2300 Maryland RoadWillow Grove, PA 19090(215) 657-6040

Booth No. 236TRl-STATE MOTOR TRANSIT CO.P.O. Box 113Joplin, MO 64802(800) 641-7582

Booth No, 432-34• 'HOFfMAN FrLTIR CORP.22795 Heslip DriveNovi, MI 48050(313) 348-7955

Booth No. 505"VALMIT100 Production CourtNew Britain, CT 06051(203) 223-6784

Booth No. 120ITW ILLINOIS TOOL WORKS3601 W. Touhy Ave.lincolnwood, IL 60645(312) 675-2100

Booth No. 543-45-47NORMAC, INC.P.O. Box 69Airport Road Ind ..ParkArden. NC 20704(704) 684-1002

Booth No. 143"WMW570 Bradley Hill Rd.Blauvelt. NY 10013(914) 358-3330

•,

FOR'M' - A"S'TER'" ' I ' , ' " " ".",' " II

, _ ' '_ _' I 1800th#'545

EASY TO INSTALIL- IBecause of its small size and weight, the FO'RMASTER does not re-quire major machine modUicationsand can be instaUed on nearly any g'rinder. Installatlon canusually be aecompllshed in less than a day,. -EAS,Y TO OPiERAJE - Two axis d,esi'gn slrrrplltles prog'ramming and operation. You canchoose between four pepular controls that feature menu and G·Code programming, graphicslrnutatlon, automatic comer rounding, automatic dlamond thickness compensation", and:more.

MADE IIINIU.S,.A.,

Patent No. 4,559',919

IMPIROVES ACCURACY

RE!DUCES WH'EELDRESSIING TIME

,ACCUIRATE - To withinl:!: .00011"of proqrarnrned dtmenslon, wiith repeat accuracy to within.00006". Extra preclslon roller bearing ways, pre-loaded roller screws and optical linearenccders.as well assuperlor ,design and construction, give the FOR,MASTERthe ability to holdinspection 9,age accuracy.PRODUCTIVE - No templates or speelal diamond reus are needed, so lead times and teet-ing Inventories are reduced, Most forms can be programmed and dressed in, ready to, grind in30 to 45 minutes. Refreshiing the form between grindin,g passes is accornpllshed iln seconds.ViERSA.TIIlE - Oan bel used with single point diamonds or with optionall Irotary d:iamondwhee!11attachment. Nearily any form can Ibedressed: quickly, easi!ly and accurately ...DURABLE - !-'lIardseats are cll:osely fitted and are air purged to totally exdude contamina-tion. Sealed servo motors.autcmatlc lubrication and totally enclosed encoders minimize downtime and ensure long service llte.

P.O.IBox 69Arden, NIC 28,'704(704) 684~1002' -,ORMAC

P,.O",Box 207Northvme, MI48167

(3113)349·2644

CIRCLE A·33 .oN READER REPLYCARD

With ad~nced. technology, Milsllbishirealized a High Speed, High AccuracyGear Hobbingand Gear Sbapillg Machinein a real. compact design.III the bobbing machine, Mitsubishi-developed feed. forward servo system

gives high speed synchronization of hoband table and the silent shaft mechanismprovides 2000 strokes per minute speedwith unnoticeable vibration to theshaping machine.Side.by·side installation is made p<Jssible

due to the flush side surfaces.An advantageous feature for designingFMS production lines.For more exciting details, please contactour office below.

10IAiHO:BGB10'CNC

, MIIITSUBISH,I,,_ HEAVY IIINIDUSTRiIES. LTD.

5-1, Marunouchl 2-chome, Chiyoda-ku. Tokyo. JapanGable Address: HISHIJU IDKYO

..

O:IASH'APES'C115CN'C-.,-...

See US at Boothl #311.

Mitsubishi IHeavy Ind'usuies America, Inc.873 Supreme Drive, Bensenville, Il60160 Phone: (312) 860-4220

Mitsubishllntemational Corporation,873 Supreme Drive, Bensenville, IL '60160 Phone: (312) 860·<1222